Quantum entanglement and interference at 3 μm

Abstract

Given the important advantages of the mid-infrared optical range (2.5 to 25 μm) for biomedical sensing, optical communications, and molecular spectroscopy, extending quantum information technology to this region is highly attractive. However, the development of mid-infrared quantum information technology is still in its infancy. Here, we report on the generation of a time-energy entangled photon pair in the mid-infrared wavelength band. By using frequency upconversion detection technology, we observe the two-photon Hong-Ou-Mandel interference and demonstrate the time-energy entanglement between twin photons at 3082 nm via the Franson-type interferometer, verifying the indistinguishability and nonlocality of the photons. This work is very promising for future applications of optical quantum technology in the mid-infrared band, which will bring more opportunities in the fields of quantum communication, precision sensing, and imaging.

The time-energy entanglement and interference between twin photons in MIR band has been demonstrated by using UCD.

INTRODUCTION

Currently, the generation, manipulation and detection of near-infrared (NIR) quantum light fields are relatively mature (1, 2) and have been applied in various quantum information processing tasks (3–6). Extending the principle to other wavelength bands, such as the mid-infrared (MIR) spectral region, is becoming an important research direction for a number of reasons. First, the MIR wavelength region covers the characteristic spectra of a large number of biochemical material molecules. In the past two decades, MIR light has been used for gas spectroscopic detection (7–9) in interaction with environmental gases such as CO₂, C_xH_y, NO_x, and SO_x. On the basis of the detection of specific vibrational energy levels of molecules in a target volume, such as food (10) or tissue (11), MIR spectroscopy is becoming an important tool for label-free histopathology (12–14). Quantum light source–based spectroscopy will notably enhance the time-frequency resolution of spectral measurements, which will greatly improve the understanding of microscopic processes (15, 16). Second, this spectral region covers two atmospheric communication windows, 3 to 5 μm and 8 to 14 μm. Because of the better scattering resistance of long-wavelength beams and the attenuation of solar background radiation in this region, long-distance optical communication becomes possible (17, 18). In addition, progress has been made in the transmission of low-loss MIR optical signals in guided-wave optical systems (19–21), which will help to expand the communication distance of fiber-optic networks. Whether in waveguide or free-space systems, extending quantum technology to this band is very promising. Another reason for interest in the MIR band is its close correlation with thermal radiation from room-temperature and high-temperature objects, which provides an effective means of thermal imaging (22, 23).

In all these application scenarios, highly efficient and highly sensitive MIR detectors are the basis for system operation, while nonclassical light sources will bring new opportunities in areas such as quantum communication, precision sensing, and metrology (24, 25). As a fledgling discipline, the primary problems that MIR quantum information technology needs to solve are the preparation and detection of nonclassical photonic states. Similar to its partner in NIR band, quantum light sources in the MIR region can also be generated by using spontaneously parametric processes (SPDCs) in a nonlinear crystal (26–28). Recently, there are some works about the generation and detection of MIR photon sources theoretically and experimentally (29–31), and the demonstration of quantum interference and entanglement (32). However, because of the limitations of optical devices and detector performance, research related to the generation of entanglement and photon interference in MIR band has progressed slowly in the past years. For example, the common used semiconductor-based detectors and superconducting detection technologies face challenges in improving detection efficiency and signal-to-noise ratios, and system operation is highly dependent on deep cooling, making the detection system more complicate and expensive. An effective solution is to use spectral translation technology, i.e., upconversion of MIR signals into the visible or NIR region by means of nonlinear frequency transformations (33–37). The upconversion process can preserve the quantum properties of the photons and greatly reduce the effect from the ambient thermal background radiation on the detection. The mature and efficient silicon-based detectors are readily available to match the converted photons, thus laying the foundation for the preparation and testing of MIR quantum light sources.

In this work, we report on the time-energy entanglement generation and Hong-Ou-Mandel (HOM) interference experiment in the MIR band. The photon pair at 3082 nm is generated by using SPDC process in a second-order nonlinear crystal pumped by a continuous wave laser. After that, the photons are upconverted to 798 nm for detection by sum frequency generation (SFG). We observe the HOM dip with about 80% visibility between MIR photons in a two-photon interference experiment, demonstrating the indistinguishability of the twin photons. In addition, we demonstrate the time-energy entanglement between twin photons by using an unbalanced Franson-type interferometer with a net interference visibility of 91.95 ± 5.18%. This study will pave the way for the expansion of quantum information technology into the MIR band.

Our work shows big differences compared with the previous works. Mancinelli et al. (29) reported on the coincidence measurement of correlated MIR photons at room temperature by using the spectral translation technology to reduce the influence of ambient Planck radiation. Cai et al. (31) reported on the generation of the nondegenerated correlated photon pairs using a short-pulse pump, and the signal photon between 3100 and 3800 nm was upconverted to NIR to detect. Both works above just showed that the strong time correlation between the upconverted photons can notably reduce the noise, but there is no any report on the demonstration of entanglement or nonclassical correlation between photons. Prabhakar et al. (32) reported the generation and preparation of a polarization-entangled photon pair at 2080 nm with a short-pulse pump, where the photons are detected by using a superconductive single-photon detector directly.

RESULTS

Experimental setup

The experimental setup for HOM interference is presented in Fig. 1A, which consists of four parts, corresponding to MIR entangled source preparation, HOM interferometer, SFG and coincident detection respectively, showed in different color. The twin MIR photons generated via SPDC in a type II phase-matched periodically poled potassium phosphate titanate (PPKTP) crystal are separated by a polarization beam splitter (PBS) and fed into a Mach-Zehnder interferometer, subsequently interferes at a 57:43 beam splitter (BS). The reflected and transmitted photons are fed into two separate upconversion detection (UCD) modules pumped by a 1077-nm laser from a Yb-doped fiber amplifier. To demonstrate time-energy entanglement, the generated MIR photons are passed through an unequal-arm Franson-type interferometer, as shown in Fig. 1B.

Fig. 1. Schematic diagram of experimental setups.

(A) Experimental setup of HOM interference. L terms, lenses; DM, dichromatic mirror; PBS, polarization beam splitter; PPKTP, periodically poled potassium phosphate titanate; PPLN, periodically poled lithium niobate crystal; OC, optical coupler. (B) Schematic diagram for demonstrating the time-energy entanglement. PZT, piezoelectric transducer; PD, photoelectric detector.

The performance of the UCD

We evaluate the performance of the UCD by testing the quantum conversion efficiency (QCE) using a classical signal source, the results are shown in Fig. 2A. We achieve a power efficiency of 146.4% or a quantum efficiency of 37.9% when the pump power is increased to be approximately 45 W. In the subsequent photon coincidence measurements, the pump laser is split equally into two UCD modules, thus resulting in a halving of the conversion efficiency. Next, to ensure that the quantum source produces degenerate photon pairs, the SPDC crystal is firstly reverse-pumped by a 3082-nm laser generated via a difference-frequency generation process to obtain its second harmonic wave at 1541 nm. The spectrum of the second harmonic wave is shown in Fig. 2B. By this way, the exact wavelength of the pump laser and the matching temperature of the crystal for the degenerate SPDC process are determined. The optical bandwidth of the SPDC is calculated to be 4 nm, while the conversion bandwidth of the subsequent SFG process is 3 nm, which allows high conversion efficiency to be achieved under the precise temperature control of the crystal.

Fig. 2. Performance of the UCD and coincidence measurement of MIR twin photons.

(A) Signal power/QCE as a function of the pump power. The power of the MIR signal is set to be 0.2 mW, ensuring that the nondepleted pump approximation is fulfilled. The dashed line is given by the theoretical model in the text. (B) The spectra of the second harmonic wave obtained via pumping the SPDC crystal by a MIR beam at 3082 nm. The inset shows the phase-matching behavior depending on the crystal temperature. (C) Coincidence counts and CAR curve with varying 1541 nm SPDC pump power. The pump power in the SFG progress is 4.95 W, and the single measurement time is 100 s. (D) Coincidence counts and CAR curve with varying SFG pump power at 1077 nm. The pump power in the SPDC process is 1.0 W, and the single measurement time is 100 s.

UCD coincidence measurements on MIR twin photons

Next, we performed coincidence measurements on MIR twin photons and investigated the performance of the photon source. An important parameter is the coincidence-to-accidental ratio (CAR). Accidental coincidence counting comes from photons that happen to arrive at the detector at the same time but generated by different SPDC process and thus cannot be attributed to correlated photons. The CAR values are given for different pump powers in the SPDC process in Fig. 2C, with an integration time of 100 s and a coincidence window of 1 ns. The CAR firstly increases monotonically with the increase of the pump power; however, when the pump power increases beyond a certain threshold, the CAR rapidly decreases. This is due to the growing multiphoton emission in the SPDC process, which leads to an increase in uncorrelated coincidence counts, negatively affecting the CAR (38, 39). Figure 2D shows the CAR at different SFG pumping powers. At low pump powers, the noise comes mainly from the detector itself and the background, while as the pump power increases, the noise caused by unintended nonlinear optical processes begins to dominate (40, 41). We lastly obtain a maximum CAR close to 100 with an SPDC pump power of 1 W and an SFG pump power of 5 W.

HOM interference on MIR twin photons

To verify the indistinguishability of the MIR photon pairs generated by the photon source, we next perform the HOM interference experiment. Twin photons generated via the SPDC are firstly separated by the PBS, and the photon in the H-polarization is rotated to the V-polarization by a half-wave plate (HWP), then these twin photons are injected into a BS. Ideally, two-photon interference will occur at the BS. Figure 3A shows the HOM interference curve obtained by moving the displacement stage in the Ι path. For quantum interference experiments based on frequency conversion techniques, Gaussian functions are chosen here for the fit (42, 43). We choose a higher pump power than that under the optimal pumping conditions of CAR shown before for our tests here to reduce the time for coincidence measurement. The fitted curve shows a full width of the half-height of the HOM dip to be 0.7 mm, giving a calculated optical bandwidth of 4.1 nm. The interference fringe has a raw (net) visibility of 80.00 ± 4.33% (85.31 ± 4.25%). Because the BS in Fig. 1 is designed for a broad band, its beam splitting ratio at the photon wavelengths in the experiment is measured to be 57:43; therefore, the theoretical limit of visibility calculated from this is 93.34%. Our results also clearly show that there is nonclassical correlation between twin photons.

Fig. 3. The results of HOM interference and time-energy entanglement.

(A) The two-photon interference curve (HOM dip) obtained from the tests, including the experimental data points and the fitted curve. The pump powers for the SPDC and SFG processes are 2.5 W and 7.4 W, respectively, and the integration time is 12 s for a single data point. The nonlinear QCE is 6.0% and the overall detection efficiency is 3.1%. The error bars are given based on a Poisson distribution. (B) Result of the coincidence counts for the maximum and minimum interference intensity. (C) Coincidences in 30 s as a function of the total phase for the signal and idle paths. The concidence window is 0.5 ns. C1 and C2 are the photon counts for each detector, respectively.

Time-energy entanglement between MIR twin photons

The generation of entangled photon pairs is a central pillar in the development of quantum information technologies such as quantum key distribution. In this work, we prepare the time-energy entangled twin photons in MIR. The experimental setup for demonstrating the time-energy entanglement is shown in Fig. 1B. After the SPDC process, the signal and idle photons are injected into an unbalanced Mach-Zehnder interferometer (UMI) with an arm difference of ΔL = 45 cm, much larger than the coherence length of the photons. An additional NIR reference light is introduced to lock the interferometer. The HWP in the long arm of the UMI is placed on a rotating translation stage, controlling the relative phase difference between the two arms. Last, the signal and idle photons are separated by a PBS and fed into two UCDs, then the coincidence measurement is performed. The coincidence measurement window is set to be 0.5 ns, shorter than ΔL/c, where c is the speed of light. The time-energy entangled state produced can be written as

$$\mid \mathrm{\phi }⟩=\frac{1}{\sqrt{2}}({\mid S⟩}_1{\mid S⟩}_2+e^{i\mathrm{\varphi }}{\mid L⟩}_1{\mid L⟩}_2)$$ (1)

where ∣L〉 and ∣S〉 denote the long and short arms of the interferometer, respectively, and ϕ = ϕ_s + ϕ_i is the relative phase of the signal and idle photons between the two arms of the UMI. Figure 3C shows the coincidence counts as a function of the phase of the interfering arms over a 30-s interval, with a raw (net) visibility of 82.47 ± 5.09% (91.95 ± 5.18%). The entangled source with a visibility of more than $1/\sqrt{2}$ clearly implies the existence of Bell nonlocality between the signal and the idle photon (44).

DISCUSSION

We generate time-energy entangled photon pairs at 3082 nm and experimentally clearly observe the HOM interference and demonstrate the time-energy entanglement between twin photons by frequency upconverting these photons to NIR at 798 nm for detection. The indistinguishability of photons in a pair is verified by two-photon interference, and the high interference visibility of the HOM dip demonstrates the possibility of using this photon source for quantum information applications in the MIR band. We have also demonstrated the time-energy entanglement between photons in the MIR band with the aid of Franson-type interferometer. Our system provides an effective alternative to single-photon detection in the MIR band with the advantages of operation at room-temperature and real-time conversion. Besides, the operating band can be easily extent by changing nonlinear crystals. As the UCD acts as a filter and the strong correlation between the upconverted photons can notably reduce the noise, it can be used in various areas such as medium wave communications, substance detection, and the development of thermal imaging cameras. Our work provides a platform for quantum optics in the MIR band and paves the way for the application of technologies such as quantum sensing and quantum-secure telecommunication.

MATERIALS AND METHODS

Details of MIR photon pair generation and measurement

The crystal for SPDC is a type II phase-matched PPKTP crystal manufactured by Raicol Crystals with dimensions of 1 mm by 2 mm by 20 mm and a poling period of 314 μm. The pump light at wavelength of 1541 nm is output from an erbium-doped fiber amplifier, adjusted by a PBS and a wave plate to meet type II phase matching requirements. Lens L1 has a focal length of 100 mm, and the beam waist of the pump is about 53 μm at the center of the PPKTP crystal. The temperature of the PPKTP crystal is precisely set to 35°C by a homemade semiconductor temperature controller to ensure the occur of the degenerate SPDC process. The generated photon pairs at 3084.2 nm are collimated through a CaF₂ lens L2 with a focal length of 100 mm. The pump light is flited by an optical band-pass filter centered at 3 μm with a bandwidth of 250 nm to prevent it from causing noise in the UCD module. The type 0 PPLN crystal for SFG has a poling period of 21.8 μm, a length of 40 mm, and an aperture of 0.5 mm by 0.5 mm, and the temperature of the crystal is set to 39.4°C. The pump light at 1077 nm used for upconversion and pump beam at 1541 nm used for SPDC process are both continuous waves. Ultimately, the upconverted 798-nm photons are collimated, filtered, and coupled into a single-mode fiber with a coupling efficiency of 79%. The silicon single-photon avalanche photodiode used has a detector quantum efficiency of 63% at 798 nm. Lens L3 has a focal length of 100 mm. The filter set consists of a dichromatic mirror, a 750-nm long-pass filter, an 850-nm short-pass filter and a band-pass filter with a bandwidth of 10 nm centered at 800 nm, which provides an attenuation of approximately 2 × 10⁻¹⁵ at 1077 nm, ensuring that residual pump light does not affect the measurement.

Quantum theory of upconversion process

The quantum theory for SFG of continuous waves in second-order nonlinear crystals is shown as follows. Three waves are involved in the upconversion process: one strong pump beam at frequency ω_p, one signal beam needed to be converted at frequency ω_s, and the upconverted beam at frequency ω_SFG, where the frequencies of the interacting waves satisfy the energy conservation ω_SFG = ω_s + ω_p, and i = s, p, SFG denotes the signal, pump, and sum-frequency photon frequencies, respectively. Under the condition of perfect phase matching and undepleted pump approximation, the associated Hamiltonian of the three-wave mixing can be written as (45)

$$\widehat{H}=i\mathrm{\hslash }{\mathit{gE}}_p ({\widehat{a}}_s{\widehat{a}}_{\mathit{SF}}^{†}-H.c.)$$ (2)

Here, g is a constant determined by the second-order polarization tensor; E_p is the electric field amplitude of the pump light; and ${\widehat{a}}_s$ and ${\widehat{a}}_{\mathit{SF}}$ are the annihilation operators of the signal photon and the upconverted photon, respectively. By solving the coupled wave equation, the analytical results of the signal and upconverted photon states are expressed as

$$\begin{array}{c}{\widehat{a}}_{\mathit{SF}}\left(L\right)=\text{sin} \left({\mathit{gE}}_{p}L\right){\widehat{a}}_s\left(0\right)+\text{cos} \left({\mathit{gE}}_{p}L\right){\widehat{a}}_{\mathit{SF}}\left(0\right)\hfill \\ {\widehat{a}}_s\left(L\right)=-\text{sin} \left({\mathit{gE}}_{p}L\right){\widehat{a}}_{\mathit{SF}}\left(0\right)+\text{cos} \left({\mathit{gE}}_{\mathit{p}}L\right){\widehat{a}}_s\left(0\right)\hfill \end{array}$$ (3)

Here, L is the length of the crystal. ${\widehat{a}}_{\mathit{SF}}(L)={\widehat{a}}_s(0)$ when gE_pL = π/2 represents the conversion of a signal photon into a corresponding upconverted photon. The quantum efficiency of upconversion is defined as η = N_SF(L)/N_s(0), where $N_i=\langle {\widehat{a}}_i^{†}{\widehat{a}}_i\rangle$ is the average number of photons measured in a certain time. When the interacting waves are all Gaussian modes, the upconversion quantum efficiency of SFG can be written as $\mathrm{\eta }={\mathrm{\eta }}_{\text{Max}}{\text{sin}}^2(\mathrm{\pi }/2\sqrt{P/P_{\text{Max}}})$ (46), where η_Max is the theoretical maximum conversion efficiency that can be achieved and P_Max is the corresponding pump optical power at this time; P is the actual pump power.

Supplementary Materials

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Supplementary Text

Figs. S1 to S3