Non-degenerated sequential time-bin entanglement generation using periodically poled KTP waveguide

Lijun Ma; Oliver Slattery; Tiejun Chang; Xiao Tang

doi:10.1364/OE.17.015799

1. Introduction

Entanglement is important for the realization of quantum communication, quantum teleportation and quantum computation. For a fiber-based quantum communications system, time-bin entanglement, or pulsed energy-time entanglement [1] is more suitable than polarization entanglement, since it is not sensitive to polarization changes in optical fibers. The original time-bin entanglement approach is realized using two consecutive laser pulses generated by an unbalanced interferometer to pump a nonlinear media. During the process, the two pulses have a certain probability to generate a photon pair by parametric down-conversion and produce the time-bin entangled photon pairs [1–4].

When a laser pulse train is used to pump the nonlinear media, and the condition $T_{c} > > τ > > τ_{p}$ , where $T_{c}$ is the coherence time of the pump beam, τis the pulse interval, and $τ_{p}$ is the pulse duration, is satisfied, a sequential time-bin entanglement can be generated [5–7]. The sequential time-bin entanglement scheme does not need an interferometer at the source side, and can achieve high-repetition rates which are more suitable for quantum communication. Several groups have successfully implemented high repetition rate sequential time-bin entanglement at the 1550 nm band using four-wave-mixing in dispersion shifted fiber [5] and spontaneous parametric down conversion in periodically-poled LiNbO₃ (PPLN) waveguides [6,7].

In this paper, we report non-degenerate sequential time-bin entanglement generation using a periodically-poled potassium titanyl phosphate (PPKTP) waveguide at a repetition rate of 1 GHz. The signal and idler photons are 895 nm and 1310 nm, which are suitable for local and long distance optical networks, respectively. The 895 nm photon is resonant with the transition line of the Cesium (Cs) atom, which may be used for quantum memory. The conjugate wavelength is 1310 nm, a suitable wavelength for long distance quantum communication in coexistence with conventional 1550 nm signals in commercial optical networks.

2. System configuration

Figure 1 schematically shows the experimental setup. A continuous wave (CW) 1064 nm laser beam is emitted from a tunable laser (New Focus: TLB 6321). The emitted beam has a narrow line-width (300 kHz), which corresponds to a coherence time of 3.3 μs. The coherence time is much longer than 1 ns and satisfies the requirement to generate 1 GHz sequential time-bin entanglement. The CW laser is modulated into a 1 GHz pulse train with a FWHM of 330 ps by an electric-optic modulator (EOM), and a RF pulse generator (Tektronix: DTG5274) provides the electrical pulse signal. Simultaneously, another channel in the pulse generator provides a 1 GHz pulse train with a FWHM of 500 ps to the up-conversion detector for pulsed-pumping, and the time delay between the two channels is adjustable. The 1064 nm optical pulses are further amplified by a fiber amplifier (IPG: YAR-1K-LP) that can control the output power. A polarization controller (PC) is used to launch the proper polarization into the first PPKTP waveguide, which is used for the second harmonic generation (SHG) of 532 nm pump pulses. The pump pulses are then coupled into a 532 nm single-mode fiber, which removes the 1064 nm light and other noise from the fiber amplifier.

Fig. 1 Experimental setup. LD: 1064 nm CW laser Diode; EOM: Electric-optic Modulator; RF: RF pulse generator; PC: Polarization controller, PPKTP: Periodically-poled KTP waveguide; DBS: 895 nm and 1310 nm dichroic beam splitter; IF: Interference filter; FC: Fiber collimator; MZI: Mach-Zehnder interferometer; Si-APD: Silicon based avalanche photo diode; PPLN: Periodically-poled LiNbO₃ waveguide for frequency up-conversion; TCSPC: Time-correlated single photon counting module. Solid line: Optical path; Dash line: Electrical connection.

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The second 2 cm long PPKTP waveguide is periodically poled to convert single photons from 532 nm to 1310 nm and 895 nm, both vertically polarized, with type I phase matching. A series of time correlated photon pairs is generated in the waveguide by spontaneous parametric down conversion (SPDC). By adjusting the pump power one can have an average of 1 pair of SPDC photons per N pump pulses. Under the condition N >> 2 and $T_{c} > > τ > > τ_{p}$ (in our experiment, $T_{c}$ = 3.3 μs, τ = 1 ns, and $τ_{p}$ = 330 ps), the quantum state of the photon pair is

| Ψ 〉 = \frac{1}{\sqrt{N}} \sum_{n = 0}^{N - 1} e^{i n ϕ_{τ}} {| n τ 〉}_{s i g n a l} {| n τ 〉}_{i d l e r}

where

ϕ_{τ}

is the phase difference between consecutive pump pulses; i is the imaginary unit; and signal and idler represents the signal (895 nm) and idler (1310 nm) photons. The signal and idler photons are separated using a dichroic beam splitter, and then coupled into 895 nm and 1310 nm single mode fibers, respectively. A bandpass filter is used to reduce the residual pump photons and other noise in the 895 nm photon path, while the noise in the 1310 nm path will be filtered by the up-conversion detector itself, which will be discussed in detail later.

To measure the two-photon-interference-fringe visibility, Franson type interferometers are used [8]. We built two free-space unbalanced Mach-Zehnder interferometers (MZI) with 1 ns optical path difference. The phases of the interferometers are adjusted by a piezo nanopositioning stage. The insertion loss of the two interferometers is measured to be about 9 dB, which includes an intrinsic interferometer loss of 3 dB (in the experiment, only the photons from one output of the interferometer are sent to the detector, while the other half of the photons in the other output are lost), fiber coupling loss, losses associated with maintaining a balance between the two paths of the interferometer and losses associated with other optical components. To reduce the influences from air turbulence and environmental vibration, the two interferometers are installed in a box and then mounted on an optical table with pneumatic vibration isolators. The visibility of the two MZI’s is about 18 dB, and the visibility can be maintained for more than a half hour in our laboratory environment, which is long enough for our entanglement measurements. Temperature control is needed to achieve longer time stability.

A silicon-based avalanche photodiode (Si-APD) (PerkinElmer: SPCM-AQR-14) is used to measure photons at 895 nm, and a PPLN waveguide-based up-conversion unit with another Si-APD [9] is used for photons at 1310 nm. We previously developed an up-conversion detector, and used it in a 1310 nm QKD system [9,10]. Recently, we improved the up-conversion detector and increased its detection efficiency. The configuration of the up-conversion detector is shown in Fig. 2 . Similar to our previous implementation, the 1550 nm light is modulated by a synchronization signal and then amplified by an erbium-doped fiber amplifier (EDFA) (IPG: EAR-0.5K-C). Two 1550/1310 nm wavelength-division-multiplexer (WDM) couplers are used to remove the 1310 nm noise from the pump light, and another 1550/1310 nm WDM coupler is used to combine the 1310 nm photon under test and the 1550 nm pump light into one fiber and the combined 1310 nm photons and pump light is then coupled into a 5 cm long PPLN waveguide, where a single 1310 nm photon and one of the 1550 nm photons are converted by a sum-frequency-generation (SFG) process into a 710 nm photon for the optimal detection. Two polarization controllers are used to align the polarization state of the 1310 nm photons and pump light respectively. The main improvement in the new up-conversion detector configuration is at the output side of waveguide. In our previous up-conversion detector, the output of the PPLN waveguide is fiber coupled, which makes the detector compact. However, some noise is coupled into that same fiber, especially the second harmonic generation of the pump source at 775 nm, and therefore we needed to use several narrow bandpass filters to suppress the noise, which caused extra loss in the signal. In the new configuration, the output of the PPLN waveguide is coated with a 710 nm anti-reflection coating and the output is not coupled into a fiber, but rather left in free space. By using two dispersive prisms, the SFG photons at 710 nm are separated from both the pump beam at 1550 nm and its weak SHG noise at 775 nm, and then detected by a Si-APD. This configuration does not require fiber coupling, thus avoiding coupling loss, and only one bandpass filter is used to reduce noise. As a result, the total detection efficiency of the up-conversion detector for a certain wavelength near 1310 nm is increased to about 33%. With a pulsed pump at a wavelength longer than the detected photons, the up-conversion detector has a dark count rate as low as 2000 Hz. The detected signals are fed into a time-correlated single photon counting system (TCSPC) (PicoQuant: PicoHarp 300) for coincidence measurement.

Fig. 2 Up-conversion detector. EOM: Electric-optic Modulator; EDFA: Erbium-doped fiber amplifier; WDM: Wavelength-division multiplexing coupler; PC: Polarization controller; PPLN: Periodically-poled LiNbO3 waveguides; IF: Interference filter. Solid line: Optical fiber; Dash line: Free space optical transmission.

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Figure 3 shows the spectrum of 1310 nm photons from the SPDC that is measured by an up-conversion spectrometer [11]. The spectral linewidth of the idler photons near 1310 nm is about 2 nm (FWHM). Since the spectral width is much wider than the acceptance bandwidth of the PPLN waveguide (0.2 nm), the quantum efficiency of the up-conversion detector is reduced to 3% when it is used to detect the 1310 nm photons generated from the SPDC. However, the narrow band pass property of the up-conversion detector provides an advantage. We do not need to use any additional narrow band pass filter in the 1310 nm optical path, since other photons at different wavelength do not satisfy the quasi-phase matching (QPM) condition for conversion and therefore are not detected.

Fig. 3 A spectrum of the idler photons generated in the PPKTP waveguide near 1310 nm.

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3. Results and discussion

In our experiment, amplified 1064 nm laser pulses (average power of 180 mW) are coupled into the SHG frequency doubler. The output laser pulses, which average 0.25 mW at 532 nm, are coupled into a 532 nm single mode fiber, and then guided into the second PPKTP for SPDC. The signal and idler photons are separated by the DBS, passed through their own MZI and then detected by a Si-APD and an up-conversion detector, respectively. Figure 4 shows the histogram of coincidence photon pairs. The histogram shows three coincidence peaks, corresponding to the different optical paths in the interferometers that photon pairs pass through. The two side peaks show the coincidence when both photons from SPDC pass through different paths in the interferometers (long and short, or short and long, respectively), and there is no interference. The central peak records the coincidence counts where both photons pass through the same path, either both long paths, or both short paths. Because the two events (photons in the earlier time bin go through short and short paths, and those in the later time bin go through long and long paths) are indistinguishable and the phase difference between two adjacent time bins are constant, photon-pair interference occurs. The interference pattern can be estimated by the following equation [3]:

R_{c} ~ 1 - V \cos (θ_{s} + θ_{i} + ϕ_{τ})

where

R_{c}

is the normalized coincidence counting rate at the central peak; V is the visibility of the interference fringes;

θ_{s}

and

θ_{i}

are the phase difference between long and short paths in the interferometers for signal and idler respectively;

ϕ_{τ}

is the phase difference between consecutive pump pulses. The coherence time of the pump is much longer than the time difference of the interferometer, so

ϕ_{τ}

is a constant. Thus the interference pattern is determined by the relative phases of the two interferometers

(θ_{s} + θ_{i})

.

Fig. 4 Histogram of the coincidence counts of photon pairs after the two MZIs. The shaded area indicates the detection window (400 ps)

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We estimate the timing jitter (FWHM) of the correlated photon pairs to be about 500 ps (FWHM) from Fig. 4, which is mostly due to the timing jitter of the two Si-APDs. Since the two side peaks have long time tails, they may leak into the time bin at the center and reduce the visibility, which is usually called inter-symbol interference. In order to minimize the influence of the side peak leakage, we assigned a detection time window around the center time slot. The worst visibility occurs when we chose a detection time window with a width as long as the clock period (1 ns), due to the inter-symbol interference. Using narrower detection time windows, we can improve the visibility. At the same time, however, the measured coincident photon number is somewhat reduced. Therefore, there is a compromise to choose the optimal time window between visibility and coincident photon number. In our experiment, we find a time window of around 400 ps is optimal for the measurement, which reduces the inter-symbol interference to less than 2% and reduces the coincidence counts by only 1.5 dB. The shaded area in Fig. 4 shows the detection time window.

The interference fringe visibility, V, as appears in Eq. (2), is an important performance metric for an entangled photon source. In this sequential time-bin entanglement experiment, the influence of accidental coincidence counts on the visibility Vcan be estimated by the following equation:

V = \frac{C C_{\max} - C C_{\min}}{C C_{\max} + C C_{\min}} = \frac{C C_{e n t}}{C C_{e n t} + 2 \cdot C C_{a c c i}}

where

C C_{\max}

and

C C_{\min}

are the maximum and minimum coincidence counts in the interference pattern.

C C_{e n t}

is the coincidence counts due to entanglement and

C C_{a c c i}

is the total accidental coincidence counts.

C C_{e n t}

can be estimated by the average photon pair number per pulse, transmission loss and detection efficiency of detectors in the following equation:

C C_{e n t} = μ α_{s} η_{s} α_{i} η_{i}

where μ is the average photon pair number per pulse (about 0.08 in our case);

α_{s}

and

α_{i}

are the channel losses for signal and idler (16 dB for both channels);

η_{s}

and

η_{i}

are the quantum efficiencies of the single photon detectors for the signal and idler (40% and 3%).

The types of accidental coincidence counts in this experiment include the accidental coincidence counts caused by multi-photon pairs and inter-symbol interference, the accidental coincidence counts between dark counts and entangled photons, as well as between the dark counts of the two detectors. Therefore, the visibility estimation equation, considering the influence of all these accidental coincidence counts, can be further expressed as follows:

V = \frac{C C_{e n t}}{C C_{e n t} + 2 \cdot (C C_{m u l t i} + C C_{i s i} + 2 \cdot C C_{d a r k - p h o t o n} + 4 \cdot C C_{d a r k - d a r k})}

where

C C_{m u l t i}

represents the accidental coincidence counts caused by multi-photon pairs. Since, in our experiment, the pump coherence time is much longer than the coherence time of photon pairs, the photon pairs follow a Poissionian distribution. When the average photon pair number per pulse is much less than 1, the second order term in the Poissionian distribution (two photon pairs per pulse) is the main factor of

C C_{m u l t i}

. The accidental coincidence counts caused by inter-symbol interference,

C C_{i s i}

, can be estimated by the detectors timing jitter.

C C_{d a r k - p h o t o n}

and

C C_{d a r k - d a r k}

are the accidental coincidences between dark counts and photons from the SPDC and the accidental coincidence between the dark counts of the two detectors, respectively. In time-bin entanglement, only half of the entangled photons are indistinguishable through a Franson-type interferometer (in the central peak in Fig. 4). All the coincident counts, except for dark count, are therefore reduced by 3 dB in this way. Dark-counts in the detection window come directly from detector itself and are therefore not subjected to the 3 dB reduction. Therefore, in the equation, the accidental

C C_{d a r k - p h o t o n}

should be multiplied by 2 in order to be compared relatively to the entangled coincident count. Like wise, the accidental

C C_{d a r k - d a r k}

should be multiplied by 2 for each detector (or by 4 in total).

C C_{m u l t i}

,

C C_{i s i}

,

C C_{d a r k - p h o t o n}

and

C C_{d a r k - d a r k}

in Eq. (5) can be estimated by the follows:

\begin{array}{l} C C_{m u l t i} \approx μ^{2} α_{s} η_{s} α_{i} η_{i} \\ C C_{i s i} = γ μ α_{s} η_{s} α_{i} η_{i} \\ C C_{d a r k - p h o t o n} = μ α_{s} η_{s} D_{i} t + μ α_{i} η_{i} D_{s} t \\ C C_{d a r k - d a r k} = D_{i} D_{s} t^{_{2}} \end{array}

where γis the inter-symbol interference caused by timing jitter (about 0.02) ;

D_{s}

and

D_{i}

are the dark count rates of the single photon detectors (100 Hz and 2000 Hz for signal and idler, respectively); and t is the detection time window (400 ps).

In addition to the influence of the accidental coincidence counts, the imperfect interferometer visibility is an important factor that may deteriorate the interference fringe visibility, V. Its influence can be estimated by the following equation:

V = \frac{C C_{e n t} - C C_{i n t}}{C C_{e n t} + C C_{i n t}}

where

C C_{i n t}

is the invalid coincidence counts caused by the imperfect interferometer visibility.

C C_{i n t}

indicates either valid entanglement coincident counts that are missing (in the numerator), or invalid entanglement coincident counts that are included (in the denominator). The valid entanglement coincident counts may be missing when, for a given phase condition, an entangled photon pair should pass through the same output of their respective interferometers, but, due to imperfections in the interferometer, one of the photons leaks to the wrong output resulting in a missing registered coincidence count. In the same way, the additional invalid entanglement coincident count may occur when, for a given phase condition, an entangled photon pair should go through different outputs of their respective interferometers, but, again due to the imperfections within the interferometer, one of the photons leaks into the wrong output, resulting in an invalidly registered coincidence count. For a balanced interferometer, these leakages are equal, and can be estimated by:

C C_{i n t} = ζ C C_{e n t} = ζ μ α_{s} η_{s} α_{i} η_{i}

where ζ is the imperfection of the interferometer (0.015 based on 18 dB interferometer visibility in this experiment).

From the Eq. (5) and Eq. (7), we can obtain an estimation equation of V considering both the influences of the accidental coincidence counts and the imperfect visibility of interferometers:

V = \frac{C C_{e n t} - C C_{i n t}}{C C_{e n t} + C C_{int} + 2 \cdot C C_{m u l t i} + 2 \cdot C C_{i s i} + 4 \cdot C C_{d a r k - p h o t o n} + 8 \cdot C C_{d a r k - d a r k}}

We can further expand the equation for V in the experimental conditions by Eq. (4), 6, 8, and 9) as follows:

V = \frac{μ α_{s} η_{s} α_{i} η_{i} - ζ μ α_{s} η_{s} α_{i} η_{i}}{μ α_{s} η_{s} α_{i} η_{i} + ζ μ α_{s} η_{s} α_{i} η + 2 μ^{2} α_{s} η_{s} α_{i} η_{i} + 2 γ μ α_{s} η_{s} α_{i} η_{i} + 4 μ α_{s} η_{s} D_{i} t + 4 μ α_{i} η_{i} D_{s} t + 8 D_{i} D_{s} t^{_{2}}}

A similar equation was first proposed in ref [12]. to estimate the interference fringe visibility for degenerate time-energy entanglement. However, the equation in ref [12]. does not consider the influence of accidental coincidence counts caused by inter-symbol interference ( $C C_{i s i}$ ) in the denominator and omits the valid, but missing, entanglement coincident counts ( $C C_{i n t}$ ) in the numerator. The influence of these two factors is significant when the repetition rate is high and the visibility of the interferometers is not perfect, and therefore should be included in the estimation equation. In should be noted though that the equation in ref [12]. is only for a degenerate photon source and considers the use of the same detectors for the both photons detection. Equation (10) provides a more general and complete estimation for the interference fringe visibility for time-bin entanglement.

By applying values in our experimental condition into the Eq. (10), the calculated visibility of 80.3% is obtained. From the calculation, $C C_{m u l t i}$ , $C C_{i s i}$ and $C C_{i n t}$ are the main contributions to the imperfection of the interference fringe visibility. To further increase the visibility, it is possible to reduce the pump power and use high visibility interferometers and low timing-jitter detectors. Due to the low dark count rate of the two detectors, $C C_{d a r k - p h o t o n}$ and $C C_{d a r k - d a r k}$ do not contribute much to the degradation of visibility in this experimental configuration. However, when the entangled photon source is used for transmission over longer distances, the influence of the dark count-related noise components will be greater than other noise components.

Piezo nano-positioning stages are used to set and vary the phase of both the signal interferometer and the idler interferometer. To determine the two-photon-interference-fringe visibility of the entangled photon pairs, we measured the photon coincidence through the interferometers, in which we fixed the phase for the signal interferometer (895 nm) and varied the phase for the idler interferometer (1310 nm). To demonstrate entanglement, we set two different fixed phases for the signal and got two interference patterns with the varied phase of the idler, as shown in Fig. 5 . For each data point, we took six measurements and then calculated the average value and their standard deviation used for the error bar. The average visibility of the two curves is 79.4% without subtraction of noise, which is close to our estimated value and is well beyond the 71% visibility for violation of the Bell inequality [13]. The measurement deviation is mainly caused by the temperature fluctuation of the interferometers.

Fig. 5 Coincidence interference fringes measured in the experiments. Solid line/ triangle and dash line/square are the coincidence counts when the piezo drive voltages of 850 nm interferometer are 0 and 1 volt, respectively.

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4. Conclusion

In conclusion, we have implemented a sequential time-bin entanglement source using a PPKTP waveguide. The signal and idler photons are at 895 nm and 1310 nm, which are suitable for local and long distance optical networks, respectively. The entangled-photon-pair flux rate measured in the experiment is 650 Hz, which can be increased by reducing the loss in the transmission and in the interferometer and by using high-efficiency single photon detectors. The two-photon-interference-fringe visibility of the entangled photon pairs is 79.4% without subtraction of noise, which can be increased by reducing the pump power, using high visibility interferometers and low timing jitter detectors.

Acknowledgement

Authors would like to thank Dr. Qiang Zhang from Edward L. Ginzton Laboratory, Stanford University for useful technical discussions. This research was supported by the NIST quantum information initiative.

References and links

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Non-degenerated sequential time-bin entanglement generation using periodically poled KTP waveguide

Abstract

1. Introduction

2. System configuration

3. Results and discussion

4. Conclusion

Acknowledgement

References and links

Cited By

Figures (5)

Equations (10)

Optics Express