1. Introduction

In the field of optical experimental quantum information science, non-linear optics based polarization entangled photon pair sources continue to be an important resource for generating non-classical states of light. These sources typically create photon pairs by coherently pumping non-linear optical wavelength conversion crystals through a process called spontaneous parametric down conversion (SPDC) [1]. Subsequently, the pairs are entangled by coherently superposing two orthogonal SPDC processes in an interferometer. Milestones in source design are: the achievement of high brightness [2] , interferometric stability [3], the use of engineered phase matching [4], monolithic integration [5, 6], and the tailoring/optimization of the spatial, spectral, and temporal properties of the photon pairs that the sources produce [7, 8]. There are many different source designs described in the literature, yet all have the same basic common goal: the reliable production of high quality polarization entangled photon pairs in abundance and in a desired spatial mode.

Despite these achievements, interferometric reliability continues to pose an experimental challenge. Balancing the interferometer requires highly skilled labour and stabilizing it requires a well controlled environment. As a result, many excellent polarization entangled photon sources remain precisely where they were built: In a laboratory. The difficulty in building a reliable interferometer has also slowed the pace of research and commercialization. This points to a gap in the research market place. There is still a need for a “universal” design which can complement a host of different down conversion crystals without sacrificing performance.

One particular source design conceived of nearly a decade ago is worth re-examining. In this paper, we make a simple, yet effective modification to the design which transforms it into a truly universal source configuration – it can address a variety of phase matching scenarios while inherently maintaining interferometer balance.

The original source [9], developed by Fiorentino and Beausoleil, will be referred to as the FB source after its authors. Its salient features are briefly described here again for reference: The FB source uses a single input birefringent beam displacer to create two spatially separate, orthogonally polarized pump modes. This is followed by a wavelength conversion stage which converts the wavelength of the two pump modes using a single crystal. The final stage of the FB source is a single output beam displacer to recombine the two converted beams of light. The effective interferometer is of the Mach-Zehnder type (MZ); the source creates polarization entangled photons and is designed for Type-1 phase matching.

The FB design has the advantage of being solid state, stable, and straightforward to align but has a drawback in that there is a potential for a dispersion induced phase discrepancy (DIPD) between the pump light and the converted light if both the input and output displacers are made of the same material. The effect is a straightforward consequence of normal dispersion: In order to complete the recombination, the extra-ordinary down converted beam spends more time in the recombination displacer than the extra-ordinary pump beam spends in the input beam splitting displacer. This effectively unbalances the interferometer, degrading the coherence and the quality of entanglement. Indeed, the authors mention of the need for further refinement due to path length differences in the FB design.

One solution would be to find input and output beam displacement materials with similar dispersion for their respective wavelengths. However, these materials may not always be available. Here we propose a simple new approach which is to symmetrize the birefringent dispersion by compensating each displacer with a second element rotated by 90 degrees. This allows for any optically suitable displacement material to be used, and eliminates the need for balancing related refinement techniques. In particular, the new approach takes direct aim at addressing the aforementioned gap in the research market: It can be readily modified to support various phase matching scenarios without sacrificing performance.

2. Interferometer design

The key departure from the FB design is the symmetrization of the FB interferometer by duplicating each optical component with an orthogonally oriented counterpart. Apart from their orientation, the duplicate components are otherwise equal in all respects to their rotated counterpart: identical in length, input facet orientation (cut angle), and material. Such a requirement may seem at first to pose a challenge, but is actually easily achieved in a manufacturing setting. As a result of the component duplication, each arm of the interferometer gets its own down conversion crystal, and the input and output beams (at different wavelengths) both undergo nominally identical double displacements. The new symmetrized interferometer is aptly called a double displacement interferometer.

A detailed description of the basic interferometer is now given. To begin, the interferometer consists of an input beam displacing stage comprised of two identical but orthogonally oriented input beam displacers placed in series along the optical direction. This is followed by a wavelength conversion stage consisting of two identical but orthogonally oriented wavelength conversion crystals placed in parallel along the optical direction. The final stage is an output beam recombining stage comprised of two identical but orthogonally oriented output beam displacers placed in series along the optical direction. The major difference between the input pair of displacers and the output pair of displacers is that their lengths are chosen to minimize the DIPD.

The notion of symmetrization via double displacement not only works for the Type-1 phase matching condition, but also the other two common phase matching types: Type-0, and Type-2. Further, it can be incorporated into both frequency degenerate and frequency non-degenerate wavelength conversion scenarios. The Type-2 configuration is somewhat more complex than the basic interferometer described above, but the key concept is that for all of the 6 possible conversion scenarios there is a displacer pair for each of the pump, signal, and idler modes. To show the concept, we describe the type-0 case, for both degenerate and non-degenerate configurations in Fig. 1 and Fig. 2 respectively, and we detail the Type-2 degenerate configuration in Fig. 3.

 

Fig. 1 View of the solid state type-0 degenerate double displacement interferometer configuration. A co-ordinate system is in the bottom right corner of the figure depicting four quadrants which reference the beam position. Coherent pump light enters the double displacement separation stage in the south-east quadrant (bottom left of figure). It is shown with Diagonal (D) polarization. After traversing the first displacer, the extra-ordinary component (H) has separated from the ordinary component (V) by some distance W and has moved to the south-west quadrant. After traversing the second displacer, the extra-ordinary component (V) has separated from the ordinary component (H) by a distance $\sqrt{2W}$ and is in the north-east quadrant. The twin pump beams then undergo non-linear type-0 SPDC in their own non-linear crystal. Following SPDC, extra-ordinary converted light (HH) displaces laterally through a distance W back to the south-east quadrant in the third displacer. And after the fourth displacer, extra-ordinary (VV) light has displaced vertically through a distance W back to the south-east quadrant. This completes the interferometer. Polarization entangled photon pairs emerge from the output (top right of figure).

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Fig. 2 View of the solid state type-0 non-degenerate double displacement interferometer configuration. The optical behaviour is identical to Fig. 1 until the recombination. To recombine non-degenerate photon pairs, a dichroic mirror (DM) first separates the wavelengths of the photons into signal and idler directions. Without loss of generality, the idler beams get reflected while the signal beams continue to propagate on. The signal/idler beams recombine through a double displacement stage designed to laterally displace the signal/idler beams through a distance W. The interferometer is completed in two distinct signal and idler loops where, for each loop, the two separate conversion processes are coherently superposed. Thus, the signal and idler photons emerge from the interferometer in a polarization entangled state.

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Fig. 3 View of the solid state type-2 degenerate double displacement interferometer configuration. The optical behaviour of the interferometer is identical to Fig. 1 until the recombination. To recombine type-2 degenerate photon pairs, two displacers are placed one on top of each other and serve to displace the horizontally polarized signal/idler beams. This is followed by two displacers placed in parallel which serve to displace the vertically polarized signal/idler beams. The result is that the two separate conversion processes are coherently superposed. The signal and idler photons emerge from the interferometer in a polarization entangled state. The type-2 design has the additional benefit of spatially separating the signal and idler outputs.

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The symmetrized design manages to achieve spatial and temporal balance, for both input (pump) and output (down-converted) wavelengths. Moreover, it can be shown that, for a given length tolerance ΔL between two ‘identical’ displacers, the resulting path length difference is approximately related through a factor of ${\theta }^2/2$, where θ is the small separation angle between extra-ordinary and ordinary light in the displacer. As an example, for θ=1/5 and ΔL=25 μm, the resulting path length difference is estimated to be 0.5 μm. Thus, with standard manufacturing techniques and tolerances, actual residual interferometer imbalance of only a few micrometers (femtoseconds) can be readily achieved.

3. Experiment

To demonstrate the design, a double displacement interferometer was created using two pairs of YVO4 beam displacers and a pair of type-0 phase matched PPLN crystals producing co-linearly propagating and co-polarized photon pairs. The crystals were 30 mm in length and supported SPDC of 776 nm pump light into signal and idler modes centered near 1552 nm. Each displacer pair differed in length by no more than 3 μm. The interferometer was fiber coupled using commercially available fiber to free space focusers. The fiber type of the input focuser was polarization maintaining fiber while the fiber type of the output focuser was regular single mode fiber. The input focuser produced a measured waist of approximately 250 μm and the output focuser produced a measured waist of approximately 150 μm. These waist values and their position in the crystal were chosen using free online software available at spdcalc.com as a guide where pair production rates were compromised with heralding efficiency. To control the relative amount of pump light in each arm of the interferometer, a user rotatable zero order half wave plate (HWP) was placed between the input fiber focuser and the interferometer. Pump removal was accomplished with a piece of polished silicon acting as an absorber. Once the device was spatially aligned, the positions of all optics were made semi-permanent using optical adhesive.

After construction, the device was operated as a polarization entangled photon source by pumping at the PM fiber input using a simple 775 nm Fabry-Perot diode laser (Qphotonics QFLD-775-10SB). Polarization correlations between the down converted photons were measured using an experimental setup similar to that shown in Fig. 4, where the output fiber from the source was connected to a fiber coupled 50:50 beam splitter to divert photons into one of two possible paths called ‘Alice’ and ‘Bob’.

 

Fig. 4 The experimental setup used to validate the Double-Displacement interferometer source via a quantum state tomography experiment: Beginning with the double displacement interferometer (top) pumped by the diode laser from Qphotonics, the output of the source was sent through a single mode fiber (SMF FIBER) and into a fiber coupled 50:50 beam splitter (50/50 BS) that probabilistically separated the output for Alice and Bob. Each output was sent through separate polarization controllers to set the basis. Polarization measurements were made via two fiber coupled free space u-benches each consisting of a quarter wave plate (QWP), half wave plate (HWP) and polarizing beam splitter (PBS). The u-benches allowed Alice and Bob to individually make any one of the six canonical polarization measurements: Horizontal, Vertical, Diagonal, Anti-diagonal, Left and Right circular. Their respective photons were detected by gated single photon detectors. Alice’s gate was internally triggered, while Bob’s was triggered by a detection event from Alice.

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Both Alice and Bob were furnished with a fiber coupled polarization controller for setting the polarization basis, a fiber coupled free space optical u-bench for making the polarization measurement, and a fiber coupled single photon detector. Both u-bench’s consisted of a zero order quarter waveplate, a zero order half waveplate and a broad band anti-reflection coated (1200 nm-1600 nm) polarizing beam splitter. Alice’s u-bench output fiber was connected directly to her internally triggered (1MHz) single photon detector (IDQuantique 201) while Bob’s u-bench output fiber was first sent through a 10m delay fiber before being connected to his single photon detector (IDQ201). Finally, Bob’s detector was externally triggered by a detection event at Alice. In this configuration, Alice’s count rate allowed an inference of the sources so-called single photon count rate, while Bob’s count rate represented the sources coincidence count rate.

To characterize the polarization state of the output light, quantum state tomography was performed. The source configuration was such that the crystals were pumped approximately equally and the source output was aligned so that Alice and Bob’s H/V measurement basis roughly coincided with the nominal H/V directions defined by the crystal. A set of 36 over complete polarization measurements were made by randomly cycling both Alice and Bob’s measurement settings through one of the following six basis states:horizontal (H), vertical (V), diagonal (D), anti-diagonal (A), left circular (L) and right circular (R) polarization. A density matrix was constructed from the raw measurement data using the maximum likelihood method.

4. Results

The results of the experiment are shown in Fig. 5 and Fig. 6 showing, respectively, the real and imaginary parts of the reconstructed density matrix.

 

Fig. 5 Raw Tomographic data displaying the real part of the computed density matrix.

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Fig. 6 Raw Tomographic data displaying the imaginary part of the computed density matrix.

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A close examination of the off diagonal elements reveals the presence of significant non-classical correlations between Alice and Bob. To quantify these correlations, optimal local rotations were simulated and applied to the density matrix to best approximate one of the maximally entangled Bell states. The results of applying those rotations allowed a calculation of the entanglement fidelity with the maximally entangled state. The entanglement fidelity between the rotated state and that of the maximally entangled state is calculated to be $\ge 98\%$.

To demonstrate the design repeatability and also its manufacturability, a total of four different polarization entangled photon sources were built, each equipped with a type-0 double displacement interferometer for balanced wavelength conversion from 776 nm to 1552 nm. Each produced high quality polarization entangled states directly out of their shipping case, without the need for any optical alignment. State control and phase flipping were achieved through rotation of the user rotatable HWP, pair production rates were controlled by adjusting the pump power, and the relative phase could be directly controlled by either Alice or Bob downstream of the source. Fiber out coupling efficiency was not optimized, but was measured to be anywhere from 10% to 30%. Notably, all optical parts were available directly from stock or with slight customizations (e.g. displacer lengths).

5. Conclusions

The new double displacement symmetrization technique significantly reduces the difficulties of balancing Mach-Zehnder interferometers used for coherent wavelength conversion. Consequently, the benefits of the Mach-Zehnder configuration over existing phase stable interferometers such as the Sagnac configuration [9] can now be exploited: There are no complex bidirectional loops requiring careful alignment and dual wavelength optics. In addition, the symmetrization technique is also applicable to the vast majority of phase matching scenarios and wavelengths. Furthermore, being a bulk source inherently immune to the challenges of both stabilization and alignment, the configuration is well suited for harsher environments beyond the lab and potentially even space. The design does have the challenge of requiring a pair of identically phase matched crystals, however, this can be addressed in a straightforward manner by specifying crystals from the same processed wafer. Moreover, the design allows for individual crystal temperature tuning if further refinement is necessary. Finally, the wide component availability matched with the research grade source performance makes this double displacement interferometer design an excellent candidate to become a new benchmark design for quantum light sources.