The research is supported by the Australian Research Council Centre of Excellence for Quantum Computation and Communication Technology, project number CE110001027.

1. Some Custom-built Elements
<ol>
	<li>Ring resonators 
	In this experiment, two ring resonators that split and combine beams of different frequencies are required. The design of the cavity is shown in Fig. 2.
	<ol>
		<li>Build the resonators around a hollowed cylinder of bulk aluminum. On one end, mount two flat mirrors with identical reflectivity. On the opposite end mount a maximum reflectivity curved mirror. The mirrors do not need to be glued to the cavity spacer. With careful machining of the spacer, the end-caps are enough to hold them in place.</li>
		<li>Combine the curved mirror with an O-ring and piezoelectric actuator to allow control of the cavity resonance frequency. Place the O-ring between the mirror and the cavity spacer, with the piezo behind the mirror. Compress these elements onto the cavity spacer with the end-cap to allow for fast actuation of the end mirror. The combination of O-ring compression and high-speed piezo typically allow for control bandwidths in excess of 10 kHz. 
		Note: For this example, the spacers are about 25 cm long. This length is arbitrary, although it should be chosen so that the control and probe light are not coresonant, which means that the hyperfine splitting must not be a multiple of the free-spectral-range. Due to the ring geometry, the cavity will have nondegenerate polarization modes of different finesse. The custom coated mirrors are specified to provide a cavity of finesse around 1,000 for s-polarized light, which leads to a finesse of around 100 for p-polarized light. While these experiments are typically conducted on the low-finesse mode, the setup could easily be switched to the high-finesse mode should stronger filtering of the beams be required.</li>
	</ol>
	</li>
	<li>Design of the memory cell and its housing
	<ol>
		<li>To build the memory apparatus, use a long cell containing isotopically enhanced 87Rb along with 0.5 Torr of Kr buffer gas. In the setup, the length is 20 cm. The windows of the cell are antireflection coated. This cell must be heated to around 80 &#176;C using a nonmagnetic heating wire.</li>
		<li>Encase the cell in three concentric solenoids. The two inner solenoids create the magnetic field gradients. To wind these solenoids, perform a simulation using the Biot-Savart equation. Simulate the variable-pitch solenoid that will provide a linearly varying magnetic field.</li>
		<li>Using a graphing program, print out a plot of this spiral onto a piece of paper. Wrap the paper around a PVC pipe to provide a line to follow and wind the wire onto the pipe. Note: In this setup the coils are 50 cm long, over twice the length of the gas cell, to avoid edge effects. The diameters are 6 and 10 cm, which is twice the diameter of the cell, to ensure the magnetic fields are mostly longitudinal. The gradient solenoids oppose each other so that switching between them will switch the sign of the gradient (see Fig. 3). In a typical experiment, 2-3 A of current is run through these coils and the coils are switched in 3-4 &#181;sec. 
		</li>
		<li>To optimize the switching time and stop oscillations use 200 &#937; damping resistors in series with the coils. Place these two solenoids inside the third normally wound coil that is used to provide a DC magnetic field to lift the degeneracy of the Zeeman levels. Rubidium has a shift of about 1.4 MHz/G of magnetic field 26. A typical DC field is 6 G, while the gradients would be 2 G/m.</li>
		<li>Place two layers of &#181;-metal shielding around the three magnetic coils to reduce the influence of the Earth&#39;s magnetic field on the experiment.</li>
	</ol>
	</li>
</ol>
2. Layout of the Optical Beam Path
<ol>
	<li>Use a single mode laser tuned near the rubidium D1 line at 795 nm. Monitor the frequency of the laser using a saturated absorption measurement, as shown in Figure&#160;3. Detune the frequency by about 1.5 GHz above the F=2 to F&#39;=2 transition. This will be the approximate frequency of the control beam.</li>
	<li>At the beamsplitter BS2, tap some light off the main laser to form the control beam. Shift its frequency by using the acousto-optic modulator AOM1. This AOM also allows modulation of the control beam power. To drive the AOM, pass the output of a signal source through an RF switch that is controlled by a TTL signal, and then amplify the signal before sending it into the AOM. Fine tune the control frequency, to optimize the Raman absorption for example, by changing the drive frequency of this AOM. The RF drive frequency of the AOMs in the setup is 80 MHz, but this is arbitrary.</li>
	<li>Detune the probe beam, which will be stored in the quantum memory, by 6.8 GHz from the control beam, this frequency being the hyperfine ground state splitting of 87Rb. To prepare this frequency, pass the laser through a fiber-coupled electro-optic modulator that is driven by a 6.8 GHz microwave source. This generates an array of sidebands at harmonics of 6.8 GHz, above and below the carrier frequency.</li>
	<li>To obtain a probe beam with a pure frequency, separate the +6.8 GHz light from all the other unwanted modulation sidebands. To do this, use one of the ring cavities. Lock Cavity 1 on resonance with the +6.8 GHz sideband. This frequency will then be transmitted through the resonator, while all other frequencies are reflected, thus preparing a pure frequency that will address the F=1 ground state of the rubidium atoms. The cavity may be locked using the Pound-Drever-Hall technique 27], using the light reflected from the input mirror.</li>
	<li>Tap off a part of the laser beam at BS3 and send it through AOM2 to allow fine control of the frequency and intensity of the probe beam. There are a couple of methods available to drive the AOM. For instance, use a programmable signal generator set to generate Gaussian pulses modulated at 80 MHz. Alternatively, combine a continuous 80 MHz signal with a pulse at an RF mixer to give a pulse modulated at 80 MHz. Either way, this modulated Gaussian is then amplified and sent into the AOM to give a pulse of light into a diffracted order of the AOM. 
	Note: This diffracted order will provide finely controlled pulses of light that can be stored in the memory. The amplitude of the pulses can be tuned using a combination of the AOM drive power and varying the splitting ratio of BS1. This allows reliable production of a wide range of pulse amplitudes, and in particular, allows the production of very weak pulses with mean photon numbers less than 1 23.</li>
	<li>The next stage is to recombine the probe and control beams. This could be done with a simple beamsplitter, but that would mean losing some portion of the light. If the polarization of the probe and control were orthogonal then lossless recombination could be achieved using a polarizing beam splitter, but the storage can only truly be optimized via independent control of the probe and control polarizations.
	<ol>
		<li>To achieve this, use a second, high-efficiency, impedance-matched, ring cavity. Set up a cavity so that the probe beam is transmitted through, while the control field is reflected off the output mirror. Transmission of the probe through this second resonator also provides a second layer of frequency filtering, which helps avoid problems with four-wave mixing.</li>
		<li>Lock this cavity to the frequency of the probe beam using an auxiliary locking beam (dashed line) that is injected into the reverse mode of the cavity. Tune this beam to a different frequency, polarization and spatial mode from the probe beam so that it may be detected on reflection without adversely affecting the probe beam. The reason for this effort is that it is fiendishly difficult to use the low-power, pulsed probe beam to lock the cavity. The control and probe beams are collimated before the memory cell to 7 mm and 3 mm sizes, respectively.</li>
		<li>The control field power before the memory cell is ~270 mW and probe power may be chosen from zero to a few microwatts depending on the experiment run. Using a quarter-wave plate, adjust the polarization of the combined probe and control beams to be (approximately) circular and of the same helicity. Inject them into the memory gas cell apparatus.</li>
	</ol>
	</li>
	<li>Control the timing of all the elements of the experiment using a LabVIEW program 28. A typical duty cycle would be 120 &#181;sec. Switch the heater off during the memory storage time to avoid interference with the memory operation. A typical timing sequence is shown in Figure&#160;4. When possible, switch the control beam off while the light is stored in the memory. In a warm gas cell, although the Raman transition is detuned from the excited state beyond the Doppler width, the control field can still be a significant source of decoherence in the memory due to the non-zero probability of the spontaneous Raman scattering. The Raman scattering is directly proportional to the control field power and inversely to the detuning squared. If the control field is kept on during the entire storage time, it can interact with the two lower states and destroy the coherence with the exponential rate defined by the scattering. This is explained further in the discussion section.</li>
	<li>After storage and recall, pass the probe through a filtering cell in order to strip the control field from the beam. It is possible to use a cell with a natural mixture of Rb. The 85Rb dominates and absorbs strongly at the control beam frequency, providing 60 dB of suppression. The probe beam is attenuated much less, typically 1.4 dB. Use a cell 75 mm long, heated to 140 &#176;C. A cell with isotopically enhanced 85Rb would lead to less probe absorption.</li>
	<li>The final step is the detection of the probe pulses, using a homodyne or heterodyne detection. The advantage of this detection method is that it is mode selective so some residual control light will not impact on the measurements. The echo has a (near) circular polarization that is made linear using a half-wave/quarter-wave plate combination.
	<ol>
		<li>To produce the local oscillator, tap off a part of the beam at BS4 and shift its frequency using AOM4. Store the signal from the homodyne or heterodyne setup using a fast oscilloscope, triggered to the LabVIEW&#160;control program.</li>
	</ol>
	</li>
</ol>

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The authors declare that they have no competing financial interests.

A necessary condition for high memory efficiency is a high OD [30]. The OD of &#923;-GEM is proportional to the Raman factor &#937;_c2/&#916;2, where &#937;_c is the coupling field Rabi frequency and &#916; is the Raman detuning from the excited state. The spontaneous Raman scattering rate is also proportional to the Raman factor and there is therefore a trade-off between achieving high absorption and low scattering losses. To find the optimum settings for the control field power, detuning and gas temperature we use an iterative process. The scattering losses can be mitigated to some extent by switching off the control beam during storage, after the pulse is fully absorbed. Optical depth is also affected by the internal state of the atoms. Ideally we would like to have as many atoms as possible in the F=1 hyperfine level to increase the absorption of the probe. The control beam also plays a role here as it acts to pump atoms from the F=2 to F=1 levels. This is not very efficient, due to the detuning, but the control beam is powerful and can be left on for long periods of time between pulse storage experiments. The width of the Raman line in our experiment is around 100 kHz, which is mostly a result of power broadening caused by the control field. This almost corresponds to the rate at which atoms are pumped from the F = 2 to the F = 1 hyperfine state. However there will be some population left on mf = 2 (or -2 depending on the sign of the circular polarization) of hyperfine level F = 2 due to the lack of allowed optical transitions.
The OD will also depend strongly on the temperature of the cell, which determines the number of atoms in the gas phase. We use a temperature of around 78 &#176;C, measured at the center of the cell. We noticed that in our cell, increasing the temperature beyond 85 &#176;C can result in some absorption of the control field as well as some incoherent absorption of the probe signal. The heater is switched off during the experimental run to avoid disturbing the magnetic field inside the cell.
Polarizations of both probe and control fields also play a crucial role in the absorption efficiency of the memory. The D1 transition line of 87Rb has two hyperfine excited states with a total of 8 Zeeman sublevels. In principle, the choice of identical circular polarizations for both the probe and the control fields ensures that they only interact with the excited state level mf = 2 (or -2), F&#39; = 2. The linear or elliptical polarizations of the laser fields give rise to Raman coupling via other Zeeman sublevels of F&#39; = 1, 2. This will result in broadening and asymmetry in the Raman line shape, due to the different coupling constants and ac&#160;Stark shifts of the various transitions. Unfortunately, identically circular polarized probe and control fields prepared before the memory can experience different polarization self-rotations as they propagate through the memory. This effect is more pronounced in high OD media, which we have in our experiment. This means that fine-tuning of probe and control beam polarization is needed to counteract the impact of self-rotation.
To further complicate matters, a degenerate four-wave mixing (FWM) process can sometimes be seen when working with large OD 25. This can cause amplification and consequently introduce noise to the output state of the memory. In particular, when linear polarization is used for both the control and probe beams, the FWM effect can be greatly enhanced due to the Raman excitation through multiple excited states. The conditions under which the FWM process is either enhanced or suppressed in our system are summarized in Ref 25. The impact of FWM can be mitigated by, again, fine-tuning the polarization of the probe and control beams. In this way, FWM processes can be reduced to the point that they do not add noise to the recalled light 23. With respect to FWM, it is worth noting that both cavities play an important role in suppressing the -6.8 GHz sideband generated by the Fiber-EOM that would otherwise seed the FWM process.
Both self-rotation and FWM affect the shape of the broadened Raman line. After fine-tuning, one can achieve a quite symmetric, roughly rectangular shaped absorption feature as shown in Figure&#160;5. This contrasts with the case shown in Figure&#160;7 where polarizations were chosen to demonstrate the impact of FWM. Here the Raman feature is highly asymmetric.
As mentioned previously, a natural abundance Rb cell was used to filter the control beam and pass the probe beam to the detection section. Due to the high temperature of this cell, we noticed that air currents around the cell windows cause variation in the fringe visibility of the heterodyne detection, resulting in fluctuations of the signal. This effect has been minimized by implementing the heterodyne detection immediately after the filtering cell and reducing the air currents around the cell windows using appropriate oven design. We observed a probe loss of around 30% through the filtering cell, due to Fresnel reflections from the windows and to the absorption by 87Rb atoms in the filtering cell. This loss can potentially be reduced by using antireflection coatings on the cell windows and using pure 85Rb instead of a natural mixture of Rb.
In a warm vapor cell, diffusion is one of the main limitations to the storage time. After absorbing light, atoms can diffuse out of the coherent region, thus partially erasing the stored information. Adding a buffer gas (0.5 Torr Kr, in our experiment) reduces the effect of diffusion to some extent. Too much buffer gas, however, will increase collisional broadening 31. This increases decoherence and control field absorption, which reduces the efficiency of the pumping mentioned above. Another way to reduce the effect of transverse diffusion is to increase the interaction volume by enlarging the transverse profiles of the probe and control fields. This approach will eventually be limited by inelastic collisions with the cell walls. In this case, the cell walls may be coated with antirelaxation materials 32, 33, to provide elastic collisions on the walls and therefore enhance the atomic coherence time. By minimizing the inelastic wall collision using proper wall coatings and increasing the laser beam size to almost cover the cell cross section, one would expect minimal effects from the transverse diffusion on the storage time. Longitudinal diffusion might then become the dominant decoherence effect at long storage times. Longitudinal diffusion causes the atoms to experience different magnetic field strengths during storage time that can result in reduced rephasing efficiency. One way to control longitudinal diffusion would be to use a cold atomic ensemble, such as atoms that have been cooled in a Magneto-Optic Trap (MOT). That, however, requires a whole new layer of experimental complexity involved in controlling cold atomic cloud. This is a system we are currently evaluating in our laboratory 36.

One of the outstanding challenges facing quantum information technology is the ability to build a memory for quantum states. For photonic quantum computing 1, or a quantum repeater used in a quantum key distribution system 2, this means building a memory that can store quantum states of light 3. One of the approaches taken towards this goal is to use ensembles of atoms that can be controlled in such a way as to store and then controllably release light at some later time. Numerous techniques have been developed including electromagnetically induced transparency (EIT) 4, the atomic frequency comb (AFC) 5, 6, 7, four-wave mixing (FWM) 8, Raman absorption 9, Faraday interaction 10 and photon echo techniques 11, 12, 13, 14, 13, 15, 16, 17, 18, 19.
The focus of this paper is &#923; - Gradient Echo Memory (&#923; -GEM), which works using three-level &#39;&#923;&#39; structured atomic media. It was initially implemented in a warm Rb vapor cell in 2008 20. This scheme has been used as a random access memory for light pulses, 21, has a demonstrated efficiency as high as 87% 22, provides noiseless storage of quantum states 23 and shows some promise as a platform for nonlinear optical operations 24. We have also recently published a paper that goes into some detail about the interaction of this memory with warm atomic vapor 25.
The essence of the technique is that we prepare an ensemble of atoms that is inhomogeneously broadened so that the atoms will absorb a pulse of light. In our experiment we use Raman absorption, as shown in Figure&#160;1a. The probe light, which is to be stored, will be mapped onto the coherence between two ground states of the atoms. The broadening is provided by applying a magnetic field gradient along the direction of optical propagation, inducing a spatial gradient in the Raman absorption frequencies, as shown in Figure 1b. The different frequency components of the stored pulse are thus mapped to different spatial locations linearly along the length of the atomic ensemble. In other words, the spatial profile of the atomic spin wave that is generated by the absorption of the input pulse is proportional to the Fourier transform of the temporal profile of the input pulse. As we will outline later, it is this frequency gradient that also enables some of the interesting spectral processing capabilities of this memory. By reversing the field gradient, the evolution of the coherence of the atomic ensemble can be time-reversed. This allows for the retrieval of the pulse of light.

<table><tbody><tr><td>Titanium-sapphire laser</td><td>M Squared Lasers</td><td></td><td>SolsTiS</td></tr><tr><td>Digital oscilloscope</td><td>Lecroy</td><td></td><td>WaveRunner 44Xi-A</td></tr><tr><td>Memory cell</td><td>Triad Technology</td><td></td><td>20 cm long, &lt;sup&gt;87&lt;/sup&gt;Rb enhanced, 0.5 Torr Kr buffer gas, AR-coated</td></tr><tr><td>Filter cell</td><td>Triad Technology</td><td></td><td>7.5 cm long, natural mixture Rb, no buffer gas</td></tr><tr><td>Fiber EOM</td><td>EOSPACE</td><td></td><td>PM-0K5-10-PFA-UL</td></tr><tr><td>AOM</td><td>AA Opto-Electronic</td><td></td><td>MT80-A1-IR</td></tr><tr><td>AOM drive components</td><td>Minicircuits</td><td></td><td>Amplifier ZHL-1-2W</td></tr><tr><td></td><td>Minicircuits</td><td></td><td>Mixer ZAD-6</td></tr><tr><td></td><td>Agilent</td><td></td><td>80 MHz signal source 33250A</td></tr><tr><td>Cavities</td><td></td><td></td><td>Custom made triangular ring cavity. FSR = 600 MHz, Finesse = 100.&lt;br/&gt; Flat mirrors (for input and output) IBS coating by Advanced Thin Films. Back mirror is 1 m ROC&lt;br/&gt; Newport Supermirror (R&gt;99.97%)</td></tr><tr><td>Photodiodes</td><td>Hamamatsu</td><td></td><td>S3883</td></tr><tr><td>Current Switches</td><td>Electronic Design and Research</td><td></td><td>EDR83915/2 and EDR8276612</td></tr></tbody></table>

gradient echo quantum memory in warm atomic vapor

Gradient echo memory (GEM) is a protocol for storing optical quantum states of light in atomic ensembles. The primary motivation for such a technology is that quantum key distribution (QKD), which uses Heisenberg uncertainty to guarantee security of cryptographic keys, is limited in transmission distance. The development of a quantum repeater is a possible path to extend QKD range, but a repeater will need a quantum memory. In our experiments we use a gas of rubidium 87 vapor that is contained in a warm gas cell. This makes the scheme particularly simple. It is also a highly versatile scheme that enables in-memory refinement of the stored state, such as frequency shifting and bandwidth manipulation. The basis of the GEM protocol is to absorb the light into an ensemble of atoms that has been prepared in a magnetic field gradient. The reversal of this gradient leads to rephasing of the atomic polarization and thus recall of the stored optical state. We will outline how we prepare the atoms and this gradient and also describe some of the pitfalls that need to be avoided, in particular four-wave mixing, which can give rise to optical gain.

1. Using the Raman Absorption as a Diagnostic Tool
The first result to obtain is a Raman line absorption of the probe beam light. Optimization of this absorption feature goes a long way towards achieving the best memory performance. With the magnetic gradient coils switched off, the control frequency can be scanned in the presence of a weak continuous probe wave. The absorption of the probe beam is directly related to the optical density of the atomic cell. Based on that, the temperature of the cell, power of the control beam and single photon detuning can be optimized through an iterative process to give the best possible Raman absorption. Too much control-beam power will increase absorption, but also broaden the width of the line. When optimized, the width is of the order of 100 kHz in our system.
Switching on one of the gradient coils will broaden the Raman line. The width of the broadened absorption determines the bandwidth of the memory. A compromise then has to be made between optical density, which affects memory efficiency, and memory bandwidth. The probe transmission is shown for one of our broadened Raman lines in Figure&#160;5, where the memory bandwidth is set to about 1 MHz.
Switching on both magnetic gradient coils at the same time, the nonbroadened absorption linewidth should be recovered. Any mismatch in the current magnitude or spatial inhomogeneity of the magnetic fields will reflect directly on a broadening and distortion of the Raman absorption.
2. Pulse Storage
The simplest configuration for the memory is single pulse storage and retrieval. That would be, for instance, storing pulses of duration 2 &#181;sec and switching the magnetic gradient coils 3 &#181;sec after the pulse peak, as shown in Figure&#160;6. If the optical density is low, some light leakage will be observed depending on the optical density (OD) of the medium. Carefully tuning the memory parameters is essential to obtaining high efficiency storage. This includes the optimization of the memory cell temperature, the careful alignment between the probe and the control field, tuning the intensity of the control beam to find the best compromise between absorption and scattering, ensuring the correct polarization of the beams and tuning the frequencies of the probe and control beams. This optimization method is further explained in the discussion section. Efficiencies exceeding 80% for a storage time of 4 &#181;sec 22 can be expected when all these parameters are tuned well. The efficiency of the storage is defined as the ratio between the energy of the recalled echo and the energy of an identical pulse that has not been stored in the memory. This effectively factors out the effect of linear losses, for instance due to Fresnel reflections on the surfaces or absorption in the filtering cell. When using a heterodyne detection, the energy of the pulses is measured by squaring the heterodyne signal and measuring the areas of the pulse&#39;s envelopes.
The frequency and bandwidth of the retrieved pulse depends on the current injected into the gradient coils. Simple manipulation of these currents allows for fine tuning of the retrieved pulse. More complex spectral manipulations (such as those outlined in 29) can be done using a more advanced coil setup where the gradient along the memory can be tuned as a function of position and time independently.
<img alt="Figure 1" fo:content-width="6in" src="/files/ftp_upload/50552/50552fig1.jpg" width="500px" /> 
Figure 1.&#160;a) The level scheme within the 87Rb D1 line used in the memory. The probe light is Raman absorbed to create a coherence between the F=1 and F=2 ground-states. b) The magnetic field gradient gives spatially dependent detuning of the ground-states along the length of the cell. Reversing the gradient and turning the control beam on gives recall of the stored probe light. (Adapted from [34]).&#160;<a href="https://www-jove-com.remotexs.ntu.edu.sg/files/ftp_upload/50552/50552fig1highres.jpg" target="_blank">Click here to view larger image</a>.
<img alt="Figure 2" fo:content-width="6in" src="/files/ftp_upload/50552/50552fig2.jpg" width="500px" /> 
Figure 2.&#160;Schematic of an optical mode cleaner. Refer to the Methods section for a description. <a href="https://www-jove-com.remotexs.ntu.edu.sg/files/ftp_upload/50552/50552fig2highres.jpg" target="_blank">Click here to view larger image</a>.
<img alt="Figure 3" fo:content-width="6in" src="/files/ftp_upload/50552/50552fig3.jpg" width="500px" /> 
Figure 3.&#160;Schematic of the experimental setup. AOM = Acousto-Optic Modulator; EOM = Electro-Optic Modulator; BS=Beamsplitter; &#955;/4=Quarter-wave plate. <a href="https://www-jove-com.remotexs.ntu.edu.sg/files/ftp_upload/50552/50552fig3highres.jpg" target="_blank">Click here to view larger image</a>.
<img alt="Figure 4" fo:content-width="6in" src="/files/ftp_upload/50552/50552fig4.jpg" width="500px" /> 
Figure 4.&#160;A typical timing sequence for the memory. (Taken from 35).&#160;<a href="https://www-jove-com.remotexs.ntu.edu.sg/files/ftp_upload/50552/50552fig4highres.jpg" target="_blank">Click here to view larger image</a>.
<img alt="Figure 5" fo:content-width="6in" src="/files/ftp_upload/50552/50552fig5.jpg" width="500px" /> 
Figure 5.&#160;Typical heterodyned broadened Raman line when one of the magnetic gradient coils is switched on. The data (thin solid line) is taken using heterodyne measurement. The oscillation is due to the beat between the probe light and local oscillator light. The dashed curve shows the envelope of this data which is the shape of the broadened Raman line. (Modified from 25). <a href="https://www-jove-com.remotexs.ntu.edu.sg/files/ftp_upload/50552/50552fig5highres.jpg" target="_blank">Click here to view larger image</a>.
<img alt="Figure 6" fo:content-width="6in" src="/files/ftp_upload/50552/50552fig6.jpg" width="500px" /> 
Figure 6.&#160;Typical average-efficiency GEM echo for short storage time. The magnetic gradient coils are switched at t = 10 &#956;sec (dashed line). Red: input pulse intensity profile. Blue: intensity output of the memory, demonstrating leaked light (which is apparent under the red input pulse) and recalled echo, which appears to the right of the dashed line. <a href="https://www-jove-com.remotexs.ntu.edu.sg/files/ftp_upload/50552/50552fig6highres.jpg" target="_blank">Click here to view larger image</a>.
<img alt="Figure 7" fo:content-width="6in" src="/files/ftp_upload/50552/50552fig7.jpg" width="500px" /> 
Figure 7.&#160;Four-wave mixing effect, when scanning the Raman line, for various control field powers and cell temperatures. For this figure only, the polarizations of the control field and probe beams were chosen so that they maximize the effect. Pc is the control beam power. (Modified from 25).&#160;<a href="https://www-jove-com.remotexs.ntu.edu.sg/files/ftp_upload/50552/50552fig7highres.jpg" target="_blank">Click here to view larger image</a>.

Watch this Scientific Journal Video about Gradient Echo Quantum Memory in Warm Atomic Vapor at JoVE.com

Gradient Echo Quantum Memory in Warm Atomic Vapor

The gradient echo memory is a protocol for storing optical quantum states of light in atomic ensembles. Quantum memory is a key element of a quantum repeater, which can extend the range of quantum key distribution. We outline the operation of the scheme when implemented in a 3-level atomic ensemble.

Gradient  echo memory (GEM) is a protocol for storing optical quantum states of light in  atomic ensembles. The primary motivation for such a technology ...

gradient-echo-quantum-memory-in-warm-atomic-vapor

Nanyang Technological University

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12.7K Views.  The Australian National University. The gradient echo memory is a protocol for storing optical quantum states of light in atomic ensembles. Quantum memory is a key element of a quantum repeater, which can extend the range of quantum key distribution. We outline the operation of the scheme when implemented in a 3-level atomic ensemble.

Video: Gradient Echo Quantum Memory in Warm Atomic Vapor

Hyperpolarized Xenon for NMR and MRI Applications

Nuclear magnetic resonance (NMR) spectroscopy and imaging (MRI) suffer from intrinsic low sensitivity because even strong external magnetic fields of ~10 T generate only a small detectable net-magnetization of the sample at room temperature 1. Hence, most NMR and MRI applications rely on the detection of molecules at relative high concentration (e.g., water for imaging of biological tissue) or require excessive acquisition times. This limits our ability to exploit the very useful molecular specificity of NMR signals for many biochemical and medical applications. However, novel approaches have emerged in the past few years: Manipulation of the detected spin species prior to detection inside the NMR/MRI magnet can dramatically increase the magnetization and therefore allows detection of molecules at much lower concentration 2.
Here, we present a method for polarization of a xenon gas mixture (2-5% Xe, 10% N2, He balance) in a compact setup with a ca. 16000-fold signal enhancement. Modern line-narrowed diode lasers allow efficient polarization 7 and immediate use of gas mixture even if the noble gas is not separated from the other components. The SEOP apparatus is explained and determination of the achieved spin polarization is demonstrated for performance control of the method.
The hyperpolarized gas can be used for void space imaging, including gas flow imaging or diffusion studies at the interfaces with other materials 8,9. Moreover, the Xe NMR signal is extremely sensitive to its molecular environment 6. This enables the option to use it as an NMR/MRI contrast agent when dissolved in aqueous solution with functionalized molecular hosts that temporarily trap the gas 10,11. Direct detection and high-sensitivity indirect detection of such constructs is demonstrated in both spectroscopic and imaging mode.

The production of hyperpolarized xenon by means of spin exchange optical pumping (SEOP) is described. This method yields a ~10000-fold enhancement of the nuclear spin polarization of Xe-129 and has applications in nuclear magnetic resonance spectroscopy and imaging. Examples of gas phase and solution state experiments are given.

Nuclear magnetic resonance (NMR) spectroscopy and imaging (MRI) suffer from intrinsic low sensitivity because even strong external magnetic fields of ~10 ...

Measurement of Coherence Decay in GaMnAs Using Femtosecond Four-wave Mixing

The application of femtosecond four-wave mixing to the study of fundamental properties of diluted magnetic semiconductors ((s,p)-d hybridization, spin-flip scattering) is described, using experiments on GaMnAs as a prototype III-Mn-V system.&#160; Spectrally-resolved and time-resolved experimental configurations are described, including the use of zero-background autocorrelation techniques for pulse optimization.&#160; The etching process used to prepare GaMnAs samples for four-wave mixing experiments is also highlighted.&#160; The high temporal resolution of this technique, afforded by the use of short (20 fsec) optical pulses, permits the rapid spin-flip scattering process in this system to be studied directly in the time domain, providing new insight into the strong exchange coupling responsible for carrier-mediated ferromagnetism.&#160; We also show that spectral resolution of the four-wave mixing signal allows one to extract clear signatures of (s,p)-d hybridization in this system, unlike linear spectroscopy techniques.&#160;&#160; This increased sensitivity is due to the nonlinearity of the technique, which suppresses defect-related contributions to the optical response. This method may be used to measure the time scale for coherence decay (tied to the fastest scattering processes) in a wide variety of semiconductor systems of interest for next generation electronics and optoelectronics.

The technique of femtosecond four-wave mixing is described, including spectrally-resolved and time-resolved configurations. We illustrate the utility of this technique for the investigation of crucial physical properties in the III-V diluted magnetic semiconductors, afforded by its nonlinearity and high temporal resolution.

The application of femtosecond four-wave mixing to the study of fundamental properties of diluted magnetic semiconductors ((s,p)-d hybridization, ...

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Engineering non-classical states of the electromagnetic field is a central quest for quantum optics1,2. Beyond their fundamental significance, such states are indeed the resources for implementing various protocols, ranging from enhanced metrology to quantum communication and computing. A variety of devices can be used to generate non-classical states, such as single emitters, light-matter interfaces or non-linear systems3. We focus here on the use of a continuous-wave optical parametric oscillator3,4. This system is based on a non-linear &#967;2 crystal inserted inside an optical cavity and it is now well-known as a very efficient source of non-classical light, such as single-mode or two-mode squeezed vacuum depending on the crystal phase matching. 
Squeezed vacuum is a Gaussian state as its quadrature distributions follow a Gaussian statistics. However, it has been shown that number of protocols require non-Gaussian states5. Generating directly such states is a difficult task and would require strong &#967;3 non-linearities. Another procedure, probabilistic but heralded, consists in using a measurement-induced non-linearity via a conditional preparation technique operated on Gaussian states. Here, we detail this generation protocol for two non-Gaussian states, the single-photon state and a superposition of coherent states, using two differently phase-matched parametric oscillators as primary resources. This technique enables achievement of a high fidelity with the targeted state and generation of the state in a well-controlled spatiotemporal mode.

We describe the reliable generation of non-Gaussian states of traveling optical fields, including single-photon states and coherent state superpositions, using a conditional preparation method operated on the non-classical light emitted by optical parametric oscillators. Type-I and type-II phase-matched oscillators are considered and common procedures, such as the required frequency filtering or the high-efficiency quantum state characterization by homodyning, are detailed.

Engineering non-classical states of the electromagnetic field is a central quest for quantum optics1,2. Beyond their fundamental significance, such states ...

Silicon Metal-oxide-semiconductor Quantum Dots for Single-electron Pumping

As mass-produced silicon transistors have reached the nano-scale, their behavior and performances are increasingly affected, and often deteriorated, by quantum mechanical effects such as tunneling through single dopants, scattering via interface defects, and discrete trap charge states. However, progress in silicon technology has shown that these phenomena can be harnessed and exploited for a new class of quantum-based electronics. Among others, multi-layer-gated silicon metal-oxide-semiconductor (MOS) technology can be used to control single charge or spin confined in electrostatically-defined quantum dots (QD). These QD-based devices are an excellent platform for quantum computing applications and, recently, it has been demonstrated that they can also be used as single-electron pumps, which are accurate sources of quantized current for metrological purposes. Here, we discuss in detail the fabrication protocol for silicon MOS QDs which is relevant to both quantum computing and quantum metrology applications. Moreover, we describe characterization methods to test the integrity of the devices after fabrication. Finally, we give a brief description of the measurement set-up used for charge pumping experiments and show representative results of electric current quantization.

The fabrication process and experimental characterization techniques relevant to single-electron pumps based on silicon metal-oxide-semiconductor quantum dots are discussed.

As mass-produced silicon transistors have reached the nano-scale, their behavior and performances are increasingly affected, and often deteriorated, by ...

Sub-nanometer Resolution Imaging with Amplitude-modulation Atomic Force Microscopy in Liquid

Atomic force microscopy (AFM) has become a well-established technique for nanoscale imaging of samples in air and in liquid. Recent studies have shown that when operated in amplitude-modulation (tapping) mode, atomic or molecular-level resolution images can be achieved over a wide range of soft and hard samples in liquid. In these situations, small oscillation amplitudes (SAM-AFM) enhance the resolution by exploiting the solvated liquid at the surface of the sample. Although the technique has been successfully applied across fields as diverse as materials science, biology and biophysics and surface chemistry, obtaining high-resolution images in liquid can still remain challenging for novice users. This is partly due to the large number of variables to control and optimize such as the choice of cantilever, the sample preparation, and the correct manipulation of the imaging parameters. Here, we present a protocol for achieving high-resolution images of hard and soft samples in fluid using SAM-AFM on a commercial instrument. Our goal is to provide a step-by-step practical guide to achieving high-resolution images, including the cleaning and preparation of the apparatus and the sample, the choice of cantilever and optimization of the imaging parameters. For each step, we explain the scientific rationale behind our choices to facilitate the adaptation of the methodology to every user's specific system.

We present a method for achieving sub-nanometer resolution images with amplitude-modulation (tapping mode) atomic force microscopy in liquid. The method is demonstrated on commercial atomic force microscopes. We explain the rationale behind our choices of parameters and suggest strategies for resolution optimization.

Atomic force microscopy (AFM) has become a well-established technique for nanoscale imaging of samples in air and in liquid. Recent studies have shown ...

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving

We present a cooling method for a cold Fermi gas by parametrically driving atomic motions in a crossed-beam optical dipole trap (ODT). Our method employs the anharmonicity of the ODT, in which the hotter atoms at the edge of the trap feel the anharmonic components of the trapping potential, while the colder atoms in the center of the trap feel the harmonic one. By modulating the trap depth with frequencies that are resonant with the anharmonic components, we selectively excite the hotter atoms out of the trap while keeping the colder atoms in the trap, generating parametric cooling. This experimental protocol starts with a magneto-optical trap (MOT) that is loaded by a Zeeman slower. The precooled atoms in the MOT are then transferred to an ODT, and a bias magnetic field is applied to create an interacting Fermi gas. We then lower the trapping potential to prepare a cold Fermi gas near the degenerate temperature. After that, we sweep the magnetic field to the noninteracting regime of the Fermi gas, in which the parametric cooling can be manifested by modulating the intensity of the optical trapping beams. We find that the parametric cooling effect strongly depends on the modulation frequencies and amplitudes. With the optimized frequency and amplitude, we measure the dependence of the cloud energy on the modulation time. We observe that the cloud energy is changed in an anisotropic way, where the energy of the axial direction is significantly reduced by parametric driving. The cooling effect is limited to the axial direction because the dominant anharmonicity of the crossed-beam ODT is along the axial direction. Finally, we propose to extend this protocol for the trapping potentials of large anharmonicity in all directions, which provides a promising scheme for cooling quantum gases using external driving.

We present a parametric driving method to cool an ultracold Fermi gas in a crossed-beam optical dipole trap. This method selectively removes high-energy atoms from the trap by periodically modulating the trap depth with frequencies that are resonant with the anharmonic components of the trapping potential.

We present a cooling method for a cold Fermi gas by parametrically driving atomic motions in a crossed-beam optical dipole trap (ODT). Our method employs ...

Experimental Methods for Trapping Ions Using Microfabricated Surface Ion Traps

Ions trapped in a quadrupole Paul trap have been considered one of the strong physical candidates to implement quantum information processing. This is due to their long coherence time and their capability to manipulate and detect individual quantum bits (qubits). In more recent years, microfabricated surface ion traps have received more attention for large-scale integrated qubit platforms. This paper presents a microfabrication methodology for ion traps using micro-electro-mechanical system (MEMS) technology, including the fabrication method for a 14 &#181;m-thick dielectric layer and metal overhang structures atop the dielectric layer. In addition, an experimental procedure for trapping ytterbium (Yb) ions of isotope 174 (174Yb+) using 369.5 nm, 399 nm, and 935 nm diode lasers is described. These methodologies and procedures involve many scientific and engineering disciplines, and this paper first presents the detailed experimental procedures. The methods discussed in this paper can easily be extended to the trapping of Yb ions of isotope 171 (171Yb+) and to the manipulation of qubits.

This paper presents a microfabrication methodology for surface ion traps, as well as a detailed experimental procedure for trapping ytterbium ions in a room-temperature environment.

Ions trapped in a quadrupole Paul trap have been considered one of the strong physical candidates to implement quantum information processing. This is due ...

Resonance Fluorescence of an InGaAs Quantum Dot in a Planar Cavity Using Orthogonal Excitation and Detection

The ability to perform simultaneous resonant excitation and fluorescence detection is important for quantum optical measurements of quantum dots (QDs). Resonant excitation without fluorescence detection &#8211; for example, a differential transmission measurement &#8211; can determine some properties of the emitting system, but does not allow applications or measurements based on the emitted photons. For example, the measurement of photon correlations, observation of the Mollow triplet, and realization of single photon sources all require collection of the fluorescence. Incoherent excitation with fluorescence detection &#8211; for example, above band-gap excitation &#8211; can be used to create single photon sources, but the disturbance of the environment due to the excitation reduces the indistinguishability of the photons. Single photon sources based on QDs will have to be resonantly excited to have high photon indistinguishability, and simultaneous collection of the photons will be necessary to make use of them. We demonstrate a method to resonantly excite a single QD embedded in a planar cavity by coupling the excitation beam into this cavity from the cleaved face of the sample while collecting the fluorescence along the sample&#39;s surface normal direction. By carefully matching the excitation beam to the waveguide mode of the cavity, the excitation light can couple into the cavity and interact with the QD. The scattered photons can couple to the Fabry-Perot mode of the cavity and escape in the surface normal direction. This method allows complete freedom in the detection polarization, but the excitation polarization is restricted by the propagation direction of the excitation beam. The fluorescence from the wetting layer provides a guide to align the collection path with respect to the excitation beam. The orthogonality of the excitation and detection modes enables resonant excitation of a single QD with negligible laser scattering background.

Resonant excitation of a single self-assembled quantum dot can be achieved using an excitation mode orthogonal to the fluorescence collection mode. We demonstrate a method using the waveguide and Fabry-Perot modes of a planar microcavity surrounding the quantum dots. The method allows complete freedom in the detection polarization.

The ability to perform simultaneous resonant excitation and fluorescence detection is important for quantum optical measurements of quantum dots (QDs). ...

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

To form a coherent quantum transport in hybrid superconductor-semiconductor (S-Sm) junctions, the formation of a homogeneous and barrier-free interface between two different materials is necessary. The S-Sm junction with high interface transparency will then facilitate the observation of the induced hard superconducting gap, which is the key requirement to access the topological phases (TPs) and observation of exotic quasiparticles such as Majorana zero modes (MZM) in hybrid systems. A material platform that can support observation of TPs and allows the realization of complex and branched geometries is therefore highly demanding in quantum processing and computing science and technology. Here, we introduce a two-dimensional material system and study the proximity induced superconductivity in semiconducting two-dimensional electron gas (2DEG) that is the basis of a hybrid quantum integrated circuit (QIC). The 2DEG is a 30 nm thick In0.75Ga0.25As quantum well that is buried between two In0.75Al0.25As barriers in a heterostructure. Niobium (Nb) films are used as the superconducting electrodes to form Nb- In0.75Ga0.25As -Nb Josephson junctions (JJs) that are symmetric, planar and ballistic. Two different approaches were used to form the JJs and QICs. The long junctions were fabricated photolithographically, but e-beam lithography was used for short junctions&#8217; fabrication. The coherent quantum transport measurements as a function of temperature in the presence/absence of magnetic field B are discussed. In both device fabrication approaches, the proximity induced superconducting properties were observed in the In0.75Ga0.25As 2DEG. It was found that e-beam lithographically patterned JJs of shorter lengths result in observation of induced superconducting gap at much higher temperature ranges. The results that are reproducible and clean suggesting that the hybrid 2D JJs and QICs based on In0.75Ga0.25As quantum wells could be a promising material platform to realize the real complex and scalable electronic and photonic quantum circuitry and devices.

Quantum integrated circuits (QICs) consisting of array of planar and ballistic Josephson junctions (JJs) based on In0.75Ga0.25As two-dimensional electron gas (2DEG) is demonstrated. Two different methods for fabrication of the two-dimensional (2D) JJs and QICs are discussed followed by the demonstration of quantum transport measurements in sub-Kelvin temperatures.

To form a coherent quantum transport in hybrid superconductor-semiconductor (S-Sm) junctions, the formation of a homogeneous and barrier-free interface ...

In Situ Measurement of Vacuum Window Birefringence using 25Mg+ Fluorescence

Accurate control of the polarization states of laser light is important in precision measurement experiments. In experiments involving the use of a vacuum environment, the stress-induced birefringence effect of the vacuum windows will affect the polarization states of laser light inside the vacuum system, and it is very difficult to measure and optimize the polarization states of the laser light in situ. The purpose of this protocol is to demonstrate how to optimize the polarization states of the laser light based on the fluorescence of ions in the vacuum system, and how to calculate the birefringence of vacuum windows based on azimuthal angles of external wave plates with Mueller matrix. The fluorescence of 25Mg+ ions induced by laser light that is resonant with the transition of |32P3/2,F = 4, mF&#160;= 4<img align="center" alt="Equation 100" src="/files/ftp_upload/61175/61175img1.jpg" style="color: rgb(68, 0, 68); font-size: 18px; font-weight: 700;" />&#160;&#8594;&#160;|32S1/2,F = 3, mF&#160;= 3<img align="center" alt="Equation 100" src="/files/ftp_upload/61175/61175img1.jpg" style="color: rgb(68, 0, 68); font-size: 18px; font-weight: 700;" />&#160;is sensitive to the polarization state of the laser light, and maximum fluorescence will be observed with pure circularly polarized light. A combination of half-wave plate (HWP) and quarter-wave plate (QWP) can achieve arbitrary phase retardation and is used for compensating the birefringence of the vacuum window. In this experiment, the polarization state of the laser light is optimized based on the fluorescence of 25Mg+ ion with a pair of HWP and QWP outside the vacuum chamber. By adjusting the azimuthal angles of the HWP and QWP to obtain maximum ion fluorescence, one can obtain a pure circularly polarized light inside the vacuum chamber. With the information on the azimuthal angles of the external HWP and QWP, the birefringence of the vacuum window can be determined.

In Situ Measurement of Vacuum Window Birefringence using 25Mg+ Fluorescence

Presented here is a method to measure the birefringence of vacuum windows by maximizing the fluorescence counts emitted by Doppler cooled 25Mg+ ions in an ion trap. The birefringence of vacuum windows will change the polarization states of the laser, which can be compensated by changing the azimuthal angles of external wave plates.

Accurate control of the polarization states of laser light is important in precision measurement experiments. In experiments involving the use of a vacuum ...