This research was supported by Research Foundation for Opto-Science and Technology, Japan. We thank to Dr. Tomo Osada for the useful discussions.

The adopted procedure comprises four main stages using the overall experimental setup shown in Figure 2. The first stage was the preparation of the pump laser for SPDC. In the second stage, the optical interferometer - Sagnac interferometer was constructed using a nonlinear crystal and optical polarization components. The coincidence measurement procedure using the electrical components shown in Figure 3 was described in the third stage. Finally, the actual photon correlation data shown in Figure 4 was used to estimate the fidelity and Bell parameters of the generated unconditional polarization-entangled photons.
1. Configuration of the pump laser
<ol>
	<li>Switch on the 405 nm grating-stabilized single-frequency laser diode. Adjust the output power to a few mW by reducing the input electrical current to the laser diode and by neutral density filters.</li>
	<li>Construct an external cavity between the surface of the laser diode and the holographic grating (3,600 mm&#8722;1) to realize a single-frequency operation referred to as a spectrometer. Place the holographic grating about 45o against the laser diode surface and slowly move the screw to adjust the degree, and maximize the output power from the cavity by referring to the image of the beam.</li>
	<li>Couple a laser to the polarization-maintaining optical fiber (PMF) to run a single spatial-mode operation. Adjust the fiber coupler screws to maximize the output power from PMF using a power meter.</li>
	<li>Collimate the output laser from the PMF with a fiber coupler lens. Channel the output laser through an isolator into the center of half-wave plate (HWP), a quarter-wave plate (QWP), and a short-pass dichroic mirror (DM) as shown in Figure 2. For the purpose of generating the polarization-entangled photons with the state as in (6), set the polarization state of the pump laser with diagonal (D) by setting the HWP to 22.5o, and QWP to 0o.</li>
</ol>
2. Construction of the interferometric setup
<ol>
	<li>Place a dichroic mirror (DM), a regular mirror, a PBS, and a ppKTP crystal with dimensions: 10 mm long (crystallographic x-axis), 10 mm wide (y-axis), and 1 mm thick (z-axis) as shown in Figure 2. The PBS operates at both the wavelength of the laser (405 nm) and that of the down-converted photons (810 nm). The poling period of the ppKTP crystal is 3.425 <img alt="Equation 19" src="/files/ftp_upload/59705/59705eq19.jpg" />&#160;which is designed for the collinear type-0 SPDC with 405 nm laser pump and has an anti-reflection coating at both wavelengths.</li>
	<li>Adjust the PBS and mirrors using the pump laser (405 nm) and a reference laser (810 nm). Since the length from the input to output of the interferometer is about 600 mm, make the transmitted and reflected light from PBS parallel for more than 600 mm (desirable for a few meters) to make spatial mode matchings.</li>
	<li>Place HWP1 and HWP2 into the setup. They operate at both 405 nm and 810 nm wavelengths. Adjust the HWPs to be perpendicular to the incident light using the reflected light from the surface. Set the angle of HWP1 to 45o and HWP2 to 22.5o</li>
	<li>Place a retroreflector into the setup. Adjust the position of the retroreflector such that the clockwise (CW) and counter-clockwise (CCW) reference beams are on the same spatial mode. Place charge-coupled device (CCD) cameras on mode 1 and 2 in Figure 2 to refer the beam profiling images from the output of the interferometer. Adjust the mirror and retroreflector to make the spatial mode matching by referring the profiling images on the camera.</li>
	<li>Place a focus lens between QWP for laser and DM. Since the length from the input to output of the interferometer is about 600 mm, select a lens with a focus length of 300 mm. Empirically set the focal point of the input laser pump to not be on the exact middle point of the interferometer but to be around the generation position of the second SPDC to make same-level generation efficiency of down-converted photons between first and second SPDC.</li>
	<li>Remove the CCD camera and place QWPs, polarizers (POLs), interference filters (IFs) with an 810 nm center and 3 nm bandwidth in the mode 1 and 2 as shown in Figure 2. Adjust the optical elements to be perpendicular to the incident light using the reflected light. Couple the reference laser beams to the multimode fibers using fiber couplers for detection.</li>
	<li>Place a 300 mm focus lens between DM and QWP in mode 1 and mode 2. Make the output reference laser beams to collimate for detection.</li>
	<li>Connect the multimode fibers to the single-photon counting modules (SPCMs) constructed from Silicon (Si) avalanche photodiodes. Switch off the reference laser. Switch on the SPCMs in a darkroom condition, and count the down-converted photons.</li>
	<li>Adjust the temperature of ppKTP crystal mounted on a temperature controller by referencing the count rates of down-converted photons. The appropriate temperature is typically 25-30 &#176;C.</li>
	<li>Adjust the tilting angle of HWP1 to maximize the count rates of down-converted photons. If the count rates are too weak, measure the counts without the optical elements in mode 1 and 2.</li>
</ol>
3. Measurement procedure of the coincidence count
<ol>
	<li>Select the polarization bases in mode 1 and 2 to measure the incident polarization-entangled photons using POLs and QWPs as shown in Figure 3. For the measurement of the incident photon with H (V) base, set the QWP to 0o and the POL to 0o (90o). For the measurement of the incident photon with D (A) base, set the QWP to 0o and the POL to 45o (-45o). For the measurement of the incident photon with R (L) base, set the QWP to 45o (-45o) and the POL to 0o.</li>
	<li>Connect the transistor-transistor logic (TTL) signal generated from the SPCM in mode 2 to the start signal input of a time-to-amplitude converter (TAC), and the signal in mode 1 to the stop signal input after it has passed through the electrical delay line (Delay). TAC generates electrical signals from 0 to 10 V corresponding to the time delay between two signals.
	<ol>
		<li>In this experiment, set the time delay &#916;T as 50 ns by selecting the delay line pins. Set the display of PC to show 100 ns time range by setting the dial of TAC. Then TAC generates 5 V signals as 50 ns delay time given by the electrical delay line. Therefore the 5 V signals correspond to the coincidences at 0 ns delay time of actual pulses coming from SPCMs. The coincidences at 0 ns delay time appear in the center of the display time range as shown in Figure 3.</li>
	</ol>
	</li>
	<li>Click the start button of the software, called MAESTRO-32, to measure the pulse height distribution and record the distribution with a computer controlled (PC) multi-channel analyzer (MCA). In this experiment, set the measurement time of TAC for 30 s. Analyze the height distribution of the TAC pulses from 0 to 10 V which corresponded to a -50 to 50 ns delay time between the incident photons and the SPCMs by the setting described in step 3.2.</li>
	<li>After recording the pulse height distribution, obtain the pulse height distribution data for several polarization bases as shown in Figure 4. Select the time window to be considered for coincidence counts for the analyzation of the data. Since the width of the pulse peak is determined by the SPCM&#39;s resolution time of~1 ns, the coincidence time window is necessary to be larger than the resolution time.
	<ol>
		<li>In this experiment, choose the coincidence time window to be 10 ns. Estimate the coincidence counts by integrating the area of the time window.</li>
	</ol>
	</li>
</ol>
4. Estimation procedure of the Fidelity and Bell parameters
<ol>
	<li>Determine the polarized second-order correlations <img alt="Equation 21" src="/files/ftp_upload/59705/59705eq21v2.jpg" />&#160;and cross-polarized second-order correlations <img alt="Equation 22" src="/files/ftp_upload/59705/59705eq22v2.jpg" />, where <img alt="Equation 23" src="/files/ftp_upload/59705/59705eq23v2.jpg" />&#160;refers to the polarization states H, D, and R, and <img alt="Equation 24" src="/files/ftp_upload/59705/59705eq24v2.jpg" />&#160;refers to the cross-polarization states V, A, and L. Obtain these functions by dividing the measured coincidence counts <img alt="Equation 25" src="/files/ftp_upload/59705/59705eq25v2.jpg" />&#160;by the background level <img alt="Equation 26" src="/files/ftp_upload/59705/59705eq26v2.jpg" />. Figure 4 shows the actually measured pulse height distribution of coincidence counts with several polarization bases for 30s. 
	NOTE: For example, the coincidence counts the with polarization base HH gives <img alt="Equation 27" src="/files/ftp_upload/59705/59705eq27v2.jpg" />&#160;count/30 s for coincidence window 10 ns. The average back ground level for the coincidence window is calculated as 4.3 count/30 s. Since second-order correlations are given by <img alt="Equation 28" src="/files/ftp_upload/59705/59705eq28v2.jpg" />, the polarized second-order correlation functions with polarization base HH becomes <img alt="Equation 29" src="/files/ftp_upload/59705/59705eq29v2.jpg" />. Similarly second-order correlation functions with other polarization bases are given as: <img alt="Equation 30" src="/files/ftp_upload/59705/59705eq30v2.jpg" />, and&#160;<img alt="Equation 31" src="/files/ftp_upload/59705/59705eq31v2.jpg" /> and cross-polarized second-order correlation functions as:&#160;<img alt="Equation 32" src="/files/ftp_upload/59705/59705eq32v2.jpg" /> and <img alt="Equation 33" src="/files/ftp_upload/59705/59705eq33v2.jpg" />.</li>
	<li>Determine the degree of polarization correlation between two photons for three polarization bases defined by20,21: 
	<img alt="Equation 34" src="/files/ftp_upload/59705/59705eq34v2.jpg" />&#160; &#160;(7) 
	where&#160;<img alt="Equation 35" src="/files/ftp_upload/59705/59705eq35v2.jpg" /> refers to the polarization bases of the rectilinear (H and V), diagonal (D and A), and circular (R and L) bases. The measured second-order correlation functions give the degree of each polarization bases as follows: <img alt="Equation 36" src="/files/ftp_upload/59705/59705eq36v2.jpg" />, and <img alt="Equation 37" src="/files/ftp_upload/59705/59705eq37v2.jpg" />.</li>
	<li>Determine the fidelity of generated entangled photons. Calculate the fidelity of the polarization-entangled state with respect to the state (6) in three bases20,21: 
	<img alt="Equation 38" src="/files/ftp_upload/59705/59705eq38v2.jpg" /> 
	The measured degrees of polarization correlation was <img alt="Equation 39" src="/files/ftp_upload/59705/59705eq39v2.jpg" />. The number exceeded the classical polarization correlation limit of 0.50.</li>
	<li>Determine the Bell parameters of the generated entangled photons21. Calculate the parameters from the polarization correlations as follows 19,20: 
	<img alt="Equation 40" src="/files/ftp_upload/59705/59705eq40v2.jpg" /> 
	<img alt="Equation 41" src="/files/ftp_upload/59705/59705eq41v2.jpg" /> 
	<img alt="Equation 42" src="/files/ftp_upload/59705/59705eq42v2.jpg" /> 
	The measured bases of polarization correlation were <img alt="Equation 43" src="/files/ftp_upload/59705/59705eq43v2.jpg" />. These numbers exceed the classical parameter limit of 2 and violate the Bell inequality.</li>
</ol>

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The authors have nothing to disclose.

The critical step within the protocol is how to maximize the fidelity of the generated polarization entangled photons. The estimated fidelity and Bell parameters are currently limited, mainly because we used multimode fibers to collect the generated entangled photons. The tilting of HWP1 affected the height difference of the spatial modes between the photons of the first and second SPDC and caused a spatial-mode mismatch on the output of the Sagnac interferometer. The fidelity is expected to be higher when using single-mode fibers that filter out the spatial-mode-overlapping area of the generated first and second SPDC photons. Moreover, the birefringence effect of the ppKTP crystal affected the mode mismatch between the first and second SPDC photons. In future, we can possibly improve the parameters by using additional compensation crystals.
The significance of the protocol is to realize several properties simultaneously with respect to existing method. The source of the polarization entangled photons with the protocol have a high-emission rate, are degenerate, have a broadband distribution, and are post-selection free. The characteristic advantage of the protocol is based on the multiple quantum interference using a double-pass polarization Sagnac interferometer. The photonic system makes it possible to use the large generation efficiency of polarization entangled photons and to separate degenerate photon pairs into different optical modes with no requirement of postselection. The system of high-performance polarization entangled photons can be applied for novel photonic quantum information technologies1,2,3,4.

The entangled state of photons has attracted considerable interest in the study of local realism in quantum theory and novel applications of quantum cryptography1, quantum dense coding2, quantum repeater3, and quantum teleportation4. Spontaneous parametric down-conversion (SPDC) is a second-order nonlinear process that has been introduced to directly produce entangled photon pairs in the polarization states. Owing to the recent development in quasi-phase-matching techniques, the periodically poled KTiOPO4 (ppKTP) and LiNbO3 (ppLN) have become a standard technique5. Several types of entanglement sources are developed by combining these nonlinear crystals with a Sagnac interferometer6,7,8. In particular, the scheme with orthogonally polarized photon pairs obtained by type-II SPDC makes it possible to generate unconditional polarization-entangled photons and also separate degenerated polarization-entangled photon pairs into different optical modes without postselective detection7.
In contrast, type-0 SPDC has the advantage of a simple setup and a high-emission ratio of photon pairs9. Moreover, the generated photon pairs in type-0 SPDC show a much broader bandwidth than the photons of type-II SPDC. The total photon-pair production rate per unit pump power is two orders of magnitude higher due to its large bandwidth8. A large bandwidth of correlated photon pairs allows a very short coincidence time between the detected photon pairs. This property has led to several potential applications such as quantum optical coherence tomography10, for achieving ultrashort temporal correlations through nonlinear interactions with the flux of entangled photons11, metrology methods using the very narrow dip in quantum interference12, quantum clock synchronization13, time-frequency entanglement measurement14, and multimode frequency entanglement15. However, the scheme with ordinary type-0 SPDC requires conditional detection schemes6 or wavelength filtering8 or spatial-mode filtering to separate the generated polarization-entangled photons16.
We realized a scheme that satisfies the properties of both type-0 and type-II SPDC simultaneously based on multiple quantum interference processes17. The details of the optical system were described and experimentally used to measure the parameters that characterize the generated polarization-entangled photons using a minimum number of experimental data.
The Jones Vector of horizontal (H) and vertical (V) polarization state can be written as <img alt="Equation 1" src="/files/ftp_upload/59705/59705eq1.jpg" />&#160;and <img alt="Equation 2" src="/files/ftp_upload/59705/59705eq2.jpg" style="font-size: 14px;" />. All possible pure polarization states are constructed from coherent superpositions of these two polarization states. For example, the diagonal(D), anti-diagonal(A), right-circular(R), and left-circular(L) light, respectively, are represented by:
<img alt="Equation 3" src="/files/ftp_upload/59705/59705eq3.jpg" style="font-size: 14px; opacity: 0.9;" />,
<img alt="Equation 4" src="/files/ftp_upload/59705/59705eq4.jpg" style="font-size: 14px;" />,&#160; (1)
<img alt="Equation 5" src="/files/ftp_upload/59705/59705eq5.jpg" style="font-size: 14px;" />,&#160; and
<img alt="Equation 6" src="/files/ftp_upload/59705/59705eq6.jpg" style="font-size: 14px;" />,
H and V are called the rectilinear polarization bases. D and A are called the diagonal polarization bases. R and L are called the circular polarization bases. These pure and also mixed states of the polarization can be represented by density matrixes based on the H- and V-polarization bases18.
The operating principle of the scheme is shown in Figure 1a-e. The laser is injected into a polarization Sagnac interferometer comprised of a polarizing beam splitter (PBS), two half-wave plates set to 45o (HWP1) and 22.5o (HWP2), a ppKTP crystal, and mirrors. The polarization optics with this setup work for both the wavelength of the pump laser field and down-converted photons.
The H-component of the pump laser passes through the PBS as shown in Figure 1a and round trips the setup in a clockwise (CW) direction. The polarization of the pump laser was inverted to the diagonal (D) state through HWP2. Here the V-component of the pump laser works for down-conversion, and the generated photons are V-polarized with type-0 SPDC. The SPDC polarization state of generated photon pairs can be represented as:
<img alt="Equation 7" src="/files/ftp_upload/59705/59705eq7.jpg" />.&#160;(2)
The down-converted photon pairs are H-polarized through the HWP1 set to 45o as shown in Figure 1b, and the polarization state becomes:
<img alt="Equation 8" src="/files/ftp_upload/59705/59705eq8.jpg" style="font-size: 14px;" />. (3)
The pump laser beam again injected the inverted photon pairs into the ppKTP. The generated photon pairs from the second SPDC are both V-polarized and superposed with the photon pairs generated by the first SPDC for a collinear optical mode as shown Figure 1c. The polarization state of the photon pairs after the second SPDC is represented as:
<img alt="Equation 9" src="/files/ftp_upload/59705/59705eq9.jpg" style="font-size: 14px;" />&#160;(4)
where <img alt="Equation 10" src="/files/ftp_upload/59705/59705eq10.jpg" />&#160;is the relative phase between the photon pair from the first and second SPDC. The phase does not vary with time because it is determined by the HWP1&#39;s material dispersion between the pump laser and the down-converted photons, and adjustable by tilting HWP1. The H (V)-polarization state of the down-converted photons was inverted to A (D) state as shown in (1). The polarization state of the output photon pair from HWP2 is represented as:
<img alt="Equation 11" src="/files/ftp_upload/59705/59705eq11.jpg" />&#160; (5)
When the phase <img alt="Equation 12" src="/files/ftp_upload/59705/59705eq12.jpg" style="opacity: 0.9;" />&#160;is set by tilting HWP1, only the first term of the state (5) remains as shown in Figure 1d. This is the quantum interference process that corresponds to the reverse Hong-Ou-Mandel (HOM) interference process of the polarization bases19. When the H-photon passes through PBS and the V-photon is reflected by PBS, the polarization state of the output photon pairs from PBS is represented as&#160;<img alt="Equation 13" src="/files/ftp_upload/59705/59705eq13.jpg" style="opacity: 0.9;" /> for optical mode1 and 2 as shown in Figure 1e.
Conversely, the V-component of the pump laser was reflected by PBS as shown in Figure 1f and round tripped in a counter-clockwise (CCW) direction. Through similar multiple type-0 SPDC processes and unitary transformations, the polarization state of the output from PBS becomes <img alt="Equation 14" src="/files/ftp_upload/59705/59705eq14.jpg" style="opacity: 0.9;" />. When the polarization state of the pump laser was prepared in diagonal (D) state, the relative phase between H- and V-components of the pump laser was zero. Therefore, the output state of generated photons from CW and CCW directions are superposed with the same amplitudes and represented as:
<img alt="Equation 15" src="/files/ftp_upload/59705/59705eq15.jpg" />.&#160; (6)
The output state is a polarization-entangled state known as one of the Bell states and can be converted to other three states using the polarization optics elements7. Using the relation shown in (1), the output state <img alt="Equation 16" src="/files/ftp_upload/59705/59705eq16.jpg" style="opacity: 0.9;" />&#160;can be represented by diagonal polarization bases as:
<img alt="Equation 17" src="/files/ftp_upload/59705/59705eq17.jpg" style="opacity: 0.9;" />&#160;and by circular polarization bases as: <img alt="Equation 18" src="/files/ftp_upload/59705/59705eq18.jpg" style="opacity: 0.9;" />.

<table><tbody><tr><td>300mm fous lens</td><td>Thorlabs. INC.</td><td>AC254-300-B</td><td></td></tr><tr><td>405nm LD</td><td>Digi-Key Electronics</td><td>NV4V31SF-A-ND</td><td></td></tr><tr><td>Delay line</td><td>Ortec INC.</td><td>DB463</td><td></td></tr><tr><td>Dichroic mirror (DM)</td><td>Midwest Optical Systems INC.</td><td>SP650-25.4</td><td></td></tr><tr><td>Half-wave plate (HWP) for 405nm</td><td>Thorlabs. INC.</td><td>WPH05M-405</td><td></td></tr><tr><td>Half-wave plate (HWP) for dual wavelengths</td><td>Meadowlark Co.</td><td>DHHM-100-0405/0810?</td><td></td></tr><tr><td>Interference filter (IF)</td><td>IDEX Health &amp;amp; Science, LLC</td><td>LL01-808-12.5</td><td></td></tr><tr><td>Multi-channel analyzer (MCA)</td><td>Ortec INC.</td><td>EASY-MCA-2K</td><td>MAESTRO-32 software</td></tr><tr><td>Polarization-maintaining fiber</td><td>Thorlabs. INC.</td><td>P1-405BPM-FC-1</td><td></td></tr><tr><td>Polarizer (POL)</td><td>Meadowlark Co.</td><td>G335743000</td><td></td></tr><tr><td>ppKTP crystal</td><td>RAICOL CRYSTAL LTD.</td><td></td><td>Type-0, 3.425 microns period</td></tr><tr><td>Quarter-wave plate (QWP) for 808nm</td><td>Thorlabs. INC.</td><td>WPQ05M-808</td><td></td></tr><tr><td>Quarter-wave plate (QWP) for 405nm</td><td>Thorlabs. INC.</td><td>WPQ05M-405</td><td></td></tr><tr><td>Retroreflector</td><td>Newport Co.</td><td>U-BER 1-1S</td><td></td></tr><tr><td>Single photon counting Module (SPCM)</td><td>Laser Cpmponents LTD.</td><td>Count -100C-FC</td><td>FC connecting</td></tr><tr><td>Time-to-amplitude converter (TAC)</td><td>Ortec INC.</td><td>567</td><td></td></tr></tbody></table>

a photonic system for generating unconditional polarization-entangled photons based on multiple quantum interference

We present a high-performance source of unconditional polarization-entangled photons that have a high-emission rate, a broadband distribution, are degenerated and postselection free. The property of the source is based on the multiple quantum interference effect with a round-trip configuration of a Sagnac interferometer. The quantum interference effects make it possible to use the high generation efficiency of the polarization-entangled photons to process parametric down-conversion, and separate degenerated photon pairs into different optical modes without a postselection requirement. The principle of the optical system was described and experimentally used to measure the fidelity and Bell parameters, and also to characterize the generated polarization-entangled photons from a minimum of six combinations of polarization correlated data. The experimentally obtained fidelity and Bell parameters exceeded the classical local correlation limit and are clear evidence of the generation of unconditional polarization-entangled photons.

The optical system to generate unconditional entangled photons for polarization states based on multiple quantum interferences and detection schemes to estimate the experimental fidelity by polarization correlation of generated photon pairs was discussed. The estimated fidelity of the generated photons exceeded the classical local correlation limit of 0.50. The measured Bell parameters exceeded the classical parameter limit of 2 and violated the Bell inequality. In this paper, coincidence measurements obtained from a minimum of six combinations of polarization bases were used to evaluate these parameters. Furthermore, it is possible to completely reconstruct the density matrix of the generated polarization-entangled photons via quantum state tomography, which requires coincidence measurements of 16 combinations of polarization bases18.
<img alt="Figure 1" class="xfigimg" src="/files/ftp_upload/59705/59705fig1.jpg" /> 
Figure 1: Schematic of an integrated double-pass polarization Sagnac interferometer. (a) The generation of photon pairs after the first spontaneous parametric down-conversion (SPDC). (b) Polarization rotation of the photon pairs by a half-wave plate (HWP1). (c) The generation of photon pairs after the second SPDC. (d) The quantum interference between photon pairs of the first and second SPDC by HWP2. (e) Output photon pairs produced in the clockwise (CW) direction. (f) Output photon pairs produced in the counter-clockwise (CCW) direction. <a href="https://www-jove-com.remotexs.ntu.edu.sg/files/ftp_upload/59705/59705fig1large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 2" class="xfigimg" src="/files/ftp_upload/59705/59705fig2.jpg" /> 
Figure 2:Overall optical system for generating unconditional polarization-entangled photons. The first half-wave plate (HWP) and a quarter-wave plate (QWP) are used to set the polarization state of the pump laser passing through polarization-maintaining optical fiber (PMF). The output photons were passed through lenses, QWPs, polarizers (POLs), and interference filters (IFs) in modes 1 and 2, and detected by the single-photon counting modules (SPCM). <a href="https://www-jove-com.remotexs.ntu.edu.sg/files/ftp_upload/59705/59705fig2large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 3" class="xfigimg" src="/files/ftp_upload/59705/59705fig3.jpg" /> 
Figure 3: Overall coincidence detection system for the generated polarization-entangled photons. The electrical signals from the SPCM were used to start and stop the signal of the time-to-amplitude converter (TAC) through an electrical delay line (Delay). The pulse height distribution obtained from time difference was analyzed with a computer controlled (PC) multi-channel analyzer (MCA). <a href="https://www-jove-com.remotexs.ntu.edu.sg/files/ftp_upload/59705/59705fig3large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 4" class="xfigimg" src="/files/ftp_upload/59705/59705fig4.jpg" /> 
Figure 4: Measured time difference distributions with parallel and orthogonal polarizer settings. The combinations are horizontal (H), vertical (V), diagonal (D), anti-diagonal (A), right-circular (R), and left-circular (L) polarization bases. <a href="https://www-jove-com.remotexs.ntu.edu.sg/files/ftp_upload/59705/59705fig4large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>

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A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

We describe an optical system for the generation of unconditional polarization-entangled photons based on multiple quantum interference effects with a detection scheme to estimate the experimental fidelity of generated entangled photons.

We present a high-performance source of unconditional polarization-entangled photons that have a high-emission rate, a broadband distribution, are ...

a-photonic-system-for-generating-unconditional-polarization-entangled

Nanyang Technological University

Research

JoVE Journal

Engineering

8.4K Views.  Tokyo University of Science. We presenteren een high-performance fotonisch systeem dat gebruik maakt van meerdere quantum interferentie effect te produceren polarisatie-verstrengelde, gedegenereerde, post-selectie gratis fotonen tegen de hoge emissie snelheid met een grote breedband distributie. Onze aanpak maakt gebruik van een meervoudig omgekeerd Hong-Ou-Mandel interferentieproces om polarisatie-verstrengelde fotonen te produceren met een hoge generatie efficiëntie en betrouwbare scheiding van gedegenereerde fotonpar...

Video: A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Micropunching Lithography for Generating Micro- and Submicron-patterns on Polymer Substrates

Conducting polymers have attracted great attention since the discovery of high conductivity in doped polyacetylene in 19771. They offer the advantages of low weight, easy tailoring of properties and a wide spectrum of applications2,3. Due to sensitivity of conducting polymers to environmental conditions (e.g., air, oxygen, moisture, high temperature and chemical solutions), lithographic techniques present significant technical challenges when working with these materials4. For example, current photolithographic methods, such as ultra-violet (UV), are unsuitable for patterning the conducting polymers due to the involvement of wet and/or dry etching processes in these methods. In addition, current micro/nanosystems mainly have a planar form5,6. One layer of structures is built on the top surfaces of another layer of fabricated features. Multiple layers of these structures are stacked together to form numerous devices on a common substrate. The sidewall surfaces of the microstructures have not been used in constructing devices. On the other hand, sidewall patterns could be used, for example, to build 3-D circuits, modify fluidic channels and direct horizontal growth of nanowires and nanotubes.
A macropunching method has been applied in the manufacturing industry to create macropatterns in a sheet metal for over a hundred years. Motivated by this approach, we have developed a micropunching lithography method (MPL) to overcome the obstacles of patterning conducting polymers and generating sidewall patterns. Like the macropunching method, the MPL also includes two operations (Fig. 1): (i) cutting; and (ii) drawing. The "cutting" operation was applied to pattern three conducting polymers4, polypyrrole (PPy), Poly(3,4-ethylenedioxythiophen)-poly(4-styrenesulphonate) (PEDOT) and polyaniline (PANI). It was also employed to create Al microstructures7. The fabricated microstructures of conducting polymers have been used as humidity8, chemical8, and glucose sensors9. Combined microstructures of Al and conducting polymers have been employed to fabricate capacitors and various heterojunctions9,10,11. The "cutting" operation was also applied to generate submicron-patterns, such as 100- and 500-nm-wide PPy lines as well as 100-nm-wide Au wires. The "drawing" operation was employed for two applications: (i) produce Au sidewall patterns on high density polyethylene (HDPE) channels which could be used for building 3D microsystems12,13,14, and (ii) fabricate polydimethylsiloxane (PDMS) micropillars on HDPE substrates to increase the contact angle of the channel15.

A micropunching lithography approach is developed to generate micro- and submicron-patterns on top, sidewall and bottom surfaces of polymer substrates. It overcomes the obstacles of patterning conducting polymers and generating sidewall patterns. This method allows rapid fabrication of multiple features and is free of aggressive chemistry.

Conducting polymers have attracted great attention since the discovery of high conductivity in doped polyacetylene in 19771. They offer the advantages of ...

Fabrication And Characterization Of Photonic Crystal Slow Light Waveguides And Cavities

Slow light has been one of the hot topics in the photonics community in the past decade, generating great interest both from a fundamental point of view and for its considerable potential for practical applications. Slow light photonic crystal waveguides, in particular, have played a major part and have been successfully employed for delaying optical signals1-4 and the enhancement of both linear5-7 and nonlinear devices.8-11
Photonic crystal cavities achieve similar effects to that of slow light waveguides, but over a reduced band-width. These cavities offer high Q-factor/volume ratio, for the realization of optically12 and electrically13 pumped ultra-low threshold lasers and the enhancement of nonlinear effects.14-16 Furthermore, passive filters17 and modulators18-19 have been demonstrated, exhibiting ultra-narrow line-width, high free-spectral range and record values of low energy consumption.
To attain these exciting results, a robust repeatable fabrication protocol must be developed. In this paper we take an in-depth look at our fabrication protocol which employs electron-beam lithography for the definition of photonic crystal patterns and uses wet and dry etching techniques. Our optimised fabrication recipe results in photonic crystals that do not suffer from vertical asymmetry and exhibit very good edge-wall roughness. We discuss the results of varying the etching parameters and the detrimental effects that they can have on a device, leading to a diagnostic route that can be taken to identify and eliminate similar issues.
The key to evaluating slow light waveguides is the passive characterization of transmission and group index spectra. Various methods have been reported, most notably resolving the Fabry-Perot fringes of the transmission spectrum20-21 and interferometric techniques.22-25 Here, we describe a direct, broadband measurement technique combining spectral interferometry with Fourier transform analysis.26 Our method stands out for its simplicity and power, as we can characterise a bare photonic crystal with access waveguides, without need for on-chip interference components, and the setup only consists of a Mach-Zehnder interferometer, with no need for moving parts and delay scans.
When characterising photonic crystal cavities, techniques involving internal sources21 or external waveguides directly coupled to the cavity27 impact on the performance of the cavity itself, thereby distorting the measurement. Here, we describe a novel and non-intrusive technique that makes use of a cross-polarised probe beam and is known as resonant scattering (RS), where the probe is coupled out-of plane into the cavity through an objective. The technique was first demonstrated by McCutcheon et al.28 and further developed by Galli et al.29

Use of photonic crystal slow light waveguides and cavities has been widely adopted by the photonics community in many differing applications. Therefore fabrication and characterization of these devices are of great interest. This paper outlines our fabrication technique and two optical characterization methods, namely: interferometric (waveguides) and resonant scattering (cavities).

Slow light has been one of the hot topics in the photonics community in the past decade, generating great interest both from a fundamental point of view ...

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.

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 ...

Analysis of Contact Interfaces for Single GaN Nanowire Devices

Single GaN nanowire (NW) devices fabricated on SiO2 can exhibit a strong degradation after annealing due to the occurrence of void formation at the contact/SiO2 interface. This void formation can cause cracking and delamination of the metal film, which can increase the resistance or lead to a complete failure of the NW device. In order to address issues associated with void formation, a technique was developed that removes Ni/Au contact metal films from the substrates to allow for the examination and characterization of the contact/substrate and contact/NW interfaces of single GaN NW devices. This procedure determines the degree of adhesion of the contact films to the substrate and NWs and allows for the characterization of the morphology and composition of the contact interface with the substrate and nanowires. This technique is also useful for assessing the amount of residual contamination that remains from the NW suspension and from photolithographic processes on the NW-SiO2 surface prior to metal deposition. The detailed steps of this procedure are presented for the removal of annealed Ni/Au contacts to Mg-doped GaN NWs on a SiO2 substrate.

A technique was developed that removes Ni/Au contact metal films from their substrate to allow for the examination and characterization of the contact/substrate and contact/NW interfaces of single GaN nanowire devices.

Single GaN nanowire (NW) devices fabricated on SiO2 can exhibit  a strong degradation after annealing due to the  occurrence of void formation at the ...

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 ...

Automation of Mode Locking in a Nonlinear Polarization Rotation Fiber Laser through Output Polarization Measurements

When a laser is mode-locked, it emits a train of ultra-short pulses at a repetition rate determined by the laser cavity length. This article outlines a new and inexpensive procedure to force mode locking in a pre-adjusted nonlinear polarization rotation fiber laser. This procedure is based on the detection of a sudden change in the output polarization state when mode locking occurs. This change is used to command the alignment of the intra-cavity polarization controller in order to find mode-locking conditions. More specifically, the value of the first Stokes parameter varies when the angle of the polarization controller is swept and, moreover, it undergoes an abrupt variation when the laser enters the mode-locked state. Monitoring this abrupt variation provides a practical easy-to-detect signal that can be used to command the alignment of the polarization controller and drive the laser towards mode locking. This monitoring is achieved by feeding a small portion of the signal to a polarization analyzer measuring the first Stokes parameter. A sudden change in the read out of this parameter from the analyzer will occur when the laser enters the mode-locked state. At this moment, the required angle of the polarization controller is kept fixed. The alignment is completed. This procedure provides an alternate way to existing automating procedures that use equipment such as an optical spectrum analyzer, an RF spectrum analyzer, a photodiode connected to an electronic pulse-counter or a nonlinear detecting scheme based on two-photon absorption or second harmonic generation. It is suitable for lasers mode locked by nonlinear polarization rotation. It is relatively easy to implement, it requires inexpensive means, especially at a wavelength of 1550 nm, and it lowers the production and operation costs incurred in comparison to the above-mentioned techniques.

A protocol to detect and automate mode locking in a pre-adjusted nonlinear polarization rotation fiber laser is presented. The detection of a sudden change in the output polarization state when mode locking occurs is used to command the alignment of an intra-cavity polarization controller in order to find mode-locking conditions.

When a laser is mode-locked, it emits a train of ultra-short pulses at a repetition rate determined by the laser cavity length. This article outlines a ...

Direct Imaging of Laser-driven Ultrafast Molecular Rotation

We present a method for visualizing laser-induced, ultrafast molecular rotational wave packet dynamics. We have developed a new 2-dimensional Coulomb explosion imaging setup in which a hitherto-impractical camera angle is realized. In our imaging technique, diatomic molecules are irradiated with a circularly polarized strong laser pulse. The ejected atomic ions are accelerated perpendicularly to the laser propagation. The ions lying in the laser polarization plane are selected through the use of a mechanical slit and imaged with a high-throughput, 2-dimensional detector installed parallel to the polarization plane. Because a circularly polarized (isotropic) Coulomb exploding pulse is used, the observed angular distribution of the ejected ions directly corresponds to the squared rotational wave function at the time of the pulse irradiation. To create a real-time movie of molecular rotation, the present imaging technique is combined with a femtosecond pump-probe optical setup in which the pump pulses create unidirectionally rotating molecular ensembles. Due to the high image throughput of our detection system, the pump-probe experimental condition can be easily optimized by monitoring a real-time snapshot. As a result, the quality of the observed movie is sufficiently high for visualizing the detailed wave nature of motion. We also note that the present technique can be implemented in existing standard ion imaging setups, offering a new camera angle or viewpoint for the molecular systems without the need for extensive modification.

We present a protocol for creating a real-time movie of a molecular rotational wave packet using a high-resolution Coulomb explosion imaging setup.

We present a method for visualizing laser-induced, ultrafast molecular rotational wave packet dynamics. We have developed a new 2-dimensional Coulomb ...

Chemistry

Measurement of Quantum Interference in a Silicon Ring Resonator Photon Source

Silicon photonic chips have the potential to realize complex integrated quantum information processing circuits, including photon sources, qubit manipulation, and integrated single-photon detectors. Here, we present the key aspects of preparing and testing a silicon photonic quantum chip with an integrated photon source and two-photon interferometer. The most important aspect of an integrated quantum circuit is minimizing loss so that all of the generated photons are detected with the highest possible fidelity. Here, we describe how to perform low-loss edge coupling by using an ultra-high numerical aperture fiber to closely match the mode of the silicon waveguides. By using an optimized fusion splicing recipe, the UHNA fiber is seamlessly interfaced with a standard single-mode fiber. This low-loss coupling allows the measurement of high-fidelity photon production in an integrated silicon ring resonator and the subsequent two-photon interference of the produced photons in a closely integrated Mach-Zehnder interferometer. This paper describes the essential procedures for the preparation and characterization of high-performance and scalable silicon quantum photonic circuits.

Silicon photonic chips have the potential to realize complex integrated quantum systems. Presented here is a method for preparing and testing a silicon photonic chip for quantum measurements.

Silicon photonic chips have the potential to realize complex integrated quantum information processing circuits, including photon sources, qubit ...

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). ...

Generation and Coherent Control of Pulsed Quantum Frequency Combs

We present a method for the generation and coherent manipulation of pulsed quantum frequency combs. Until now, methods of preparing high-dimensional states on-chip in a practical way have remained elusive due to the increasing complexity of the quantum circuitry needed to prepare and process such states. Here, we outline how high-dimensional, frequency-bin entangled, two-photon states can be generated at a stable, high generation rate by using a nested-cavity, actively mode-locked excitation of a nonlinear micro-cavity. This technique is used to produce pulsed quantum frequency combs. Moreover, we present how the quantum states can be coherently manipulated using standard telecommunications components such as programmable filters and electro-optic modulators. In particular, we show in detail how to accomplish state characterization measurements such as density matrix reconstruction, coincidence detection, and single photon spectrum determination. The presented methods form an accessible, reconfigurable, and scalable foundation for complex high-dimensional state preparation and manipulation protocols in the frequency domain.

A protocol is presented for the practical generation and coherent manipulation of high-dimensional frequency-bin entangled photon states using integrated micro-cavities and standard telecommunications components, respectively.

We present a method for the generation and coherent manipulation of pulsed quantum frequency combs. Until now, methods of preparing high-dimensional ...

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

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