Orthogonal spectral coding of entangled photons

Quantum transport of high-dimensional spatial information with a nonlinear detector

Information exchange between two distant parties, where information is shared without physically transporting it, is a crucial resource in future quantum networks. Doing so with high-dimensional states offers the promise of higher information capacity and improved resilience to noise, but progress to date has been limited. Here we demonstrate how a nonlinear parametric process allows for arbitrary high-dimensional state projections in the spatial degree of freedom, where a strong coherent field enhances the probability of the process. This allows us to experimentally realise quantum transport of high-dimensional spatial information facilitated by a quantum channel with a single entangled pair and a nonlinear spatial mode detector. Using sum frequency generation we upconvert one of the photons from an entangled pair resulting in high-dimensional spatial information transported to the other. We realise a d = 15 quantum channel for arbitrary photonic spatial modes which we demonstrate by faithfully transferring information encoded into orbital angular momentum, Hermite-Gaussian and arbitrary spatial mode superpositions, without requiring knowledge of the state to be sent. Our demonstration merges the nascent fields of nonlinear control of structured light with quantum processes, offering a new approach to harnessing high-dimensional quantum states, and may be extended to other degrees of freedom too.

Linear Optical Quantum Computation with Frequency-Comb Qubits and Passive Devices

We propose a linear optical quantum computation scheme using time-frequency degrees of freedom. In this scheme, a qubit is encoded in single-photon frequency combs, and manipulation of the qubits is performed using time-resolving detectors, beam splitters, and optical interleavers. This scheme does not require active devices such as high-speed switches and electro-optic modulators and is robust against temporal and spectral errors, which are mainly caused by the detectors' finite resolution. We show that current technologies almost meet the requirements for fault-tolerant quantum computation.

Widely flexible and finely adjustable nonlocal dispersion cancellation with wavelength tuning

In fiber-based quantum information processing with energy-time entangled photon pairs, optimized dispersion compensation is vital to preserve the strong temporal correlation of the photon pairs. We propose and experimentally verify that, by simply tuning the wavelength of the entangled photon pairs, nonlocal dispersion cancellation (NDC) can provide a widely flexible and finely adjustable solution for optimizing the dispersion compensation, which cannot be reached with the traditional local dispersion cancellation (LDC) instead. By way of example, when a 50 km-long single-mode fiber (SMF) is dispersion compensated by a 6.2-km-long commercial dispersion compensating fiber (DCF) based on the LDC configuration, it will lead to an almost invariant over-compensation in the wavelength range of 1500-1600 nm which restricts the observed temporal coincidence width of the self-developed energy-time entangled photon-pairs source to a minimum of ∼110 ps. While in the NDC configuration, the dispersion compensation can be readily optimized by tuning the signal wavelength to 1565.7 nm and a minimum coincidence width of 86.1 ± 0.7 ps is observed, which is mainly limited by the jitter of the single-photon detection system. Furthermore, such optimized dispersion compensation can also be achieved as the fiber length varies from 48 km to 60 km demonstrating the wide flexibility of NDC. Thanks to these capabilities, elaborate dispersion compensation modules are no longer required, which makes NDC a more versatile tool in fiber-based quantum information and metrology applications.

Direct measurement of ultrafast temporal wavefunctions

The large capacity and robustness of information encoding in the temporal mode of photons is important in quantum information processing, in which characterizing temporal quantum states with high usability and time resolution is essential. We propose and demonstrate a direct measurement method of temporal complex wavefunctions for weak light at a single-photon level with subpicosecond time resolution. Our direct measurement is realized by ultrafast metrology of the interference between the light under test and self-generated monochromatic reference light; no external reference light or complicated post-processing algorithms are required. Hence, this method is versatile and potentially widely applicable for temporal state characterization.

Fully Arbitrary Control of Frequency-Bin Qubits

Accurate control of two-level systems is a longstanding problem in quantum mechanics. One such quantum system is the frequency-bin qubit: a single photon existing in superposition of two discrete frequency modes. In this Letter, we demonstrate fully arbitrary control of frequency-bin qubits in a quantum frequency processor for the first time. We numerically establish optimal settings for multiple configurations of electro-optic phase modulators and pulse shapers, experimentally confirming near-unity mode-transformation fidelity for all fundamental rotations. Performance at the single-photon level is validated through the rotation of a single frequency-bin qubit to 41 points spread over the entire Bloch sphere, as well as tracking of the state path followed by the output of a tunable frequency beam splitter, with Bayesian tomography confirming state fidelities F_{ρ}>0.98 for all cases. Such high-fidelity transformations expand the practical potential of frequency encoding in quantum communications, offering exceptional precision and low noise in general qubit manipulation.

Quantification of nonlocal dispersion cancellation for finite frequency entanglement

Benefiting from the unique quantum feature of nonlocal dispersion cancellation (NDC), the strong temporal correlation of frequency-entangled photon pair source can be maintained from the unavoidable dispersive propagation. It has thus played a major role in many fiber-based quantum information applications. However, the limit of NDC due to finite frequency entanglement has not been quantified. In this study, we provide a full theoretical analysis of the NDC characteristics for the photon pairs with finite frequency entanglement. Experimental examinations were conducted by using two spontaneous parametric down-conversion photon pair sources with frequency correlation and anticorrelation properties. The excellent agreement demonstrates the fundamental limit on the minimum temporal correlation width by the nonzero two-photon spectral correlation width of the paired photons, which introduces an inevitable broadening by interaction with the dispersion in the signal path. This study provides an easily accessible tool for assessing and optimizing the NDC in various quantum information applications.

Quantum Nonlocal Aberration Cancellation

Phase distortions, or aberrations, can negatively influence the performance of an optical imaging system. Through the use of position-momentum entangled photons, we nonlocally correct for aberrations in one photon's optical path by intentionally introducing the complementary aberrations in the optical path of the other photon. In particular, we demonstrate the simultaneous nonlocal cancellation of aberrations that are of both even and odd order in the photons' transverse degrees of freedom. We also demonstrate a potential application of this technique by nonlocally canceling the effect of defocus in a quantum imaging experiment and thereby recover the original spatial resolution.

Tomography and Purification of the Temporal-Mode Structure of Quantum Light

High-dimensional quantum information processing promises capabilities beyond the current state of the art, but addressing individual information-carrying modes presents a significant experimental challenge. Here we demonstrate effective high-dimensional operations in the time-frequency domain of nonclassical light. We generate heralded photons with tailored temporal-mode structures through the pulse shaping of a broadband parametric down-conversion pump. We then implement a quantum pulse gate, enabled by dispersion-engineered sum-frequency generation, to project onto programmable temporal modes, reconstructing the quantum state in seven dimensions. We also manipulate the time-frequency structure by selectively removing temporal modes, explicitly demonstrating the effectiveness of engineered nonlinear processes for the mode-selective manipulation of quantum states.

Arbitrary shaping of biphoton correlations using near-field frequency-to-time mapping

Frequency-to-time mapping (FTM) is a technique used to mirror the spectral shape of an optical waveform in the time domain. The regular approach, based on the far-field condition, requires large amounts of dispersion for successful mapping. However, when the far-field condition is insurmountable for achieving a desired temporal profile, another technique, termed near-field FTM, can be employed to assist with the mapping. For the first time, we demonstrate a shaper-assisted near-field FTM using entangled photon pairs. By pre-modifying the two-photon spectral amplitude and phase before propagating the photon pairs through dispersion, we can achieve arbitrary temporal correlations in the near-field region.

Heralded generation of high-purity ultrashort single photons in programmable temporal shapes

We experimentally demonstrate a source of nearly pure single photons in arbitrary temporal shapes heralded from a parametric down-conversion (PDC) source at telecom wavelengths. The technology is enabled by the tailored dispersion of in-house fabricated waveguides with shaped pump pulses to directly generate the PDC photons in on-demand temporal shapes. We generate PDC photons in Hermite-Gauss and frequency-binned modes and confirm a minimum purity of 0.81, even for complex temporal shapes.

Direct Characterization of Ultrafast Energy-Time Entangled Photon Pairs

Energy-time entangled photons are critical in many quantum optical phenomena and have emerged as important elements in quantum information protocols. Entanglement in this degree of freedom often manifests itself on ultrafast time scales, making it very difficult to detect, whether one employs direct or interferometric techniques, as photon-counting detectors have insufficient time resolution. Here, we implement ultrafast photon counters based on nonlinear interactions and strong femtosecond laser pulses to probe energy-time entanglement in this important regime. Using this technique and single-photon spectrometers, we characterize all the spectral and temporal correlations of two entangled photons with femtosecond resolution. This enables the witnessing of energy-time entanglement using uncertainty relations and the direct observation of nonlocal dispersion cancellation on ultrafast time scales. These techniques are essential to understand and control the energy-time degree of freedom of light for ultrafast quantum optics.

Electro-Optic Frequency Beam Splitters and Tritters for High-Fidelity Photonic Quantum Information Processing

We report the experimental realization of high-fidelity photonic quantum gates for frequency-encoded qubits and qutrits based on electro-optic modulation and Fourier-transform pulse shaping. Our frequency version of the Hadamard gate offers near-unity fidelity (0.99998±0.00003), requires only a single microwave drive tone for near-ideal performance, functions across the entire C band (1530-1570 nm), and can operate concurrently on multiple qubits spaced as tightly as four frequency modes apart, with no observable degradation in the fidelity. For qutrits, we implement a 3×3 extension of the Hadamard gate: the balanced tritter. This tritter-the first ever demonstrated for frequency modes-attains fidelity 0.9989±0.0004. These gates represent important building blocks toward scalable, high-fidelity quantum information processing based on frequency encoding.

Rapidly reconfigurable high-fidelity optical arbitrary waveform generation in heterogeneous photonic integrated circuits

This paper demonstrates rapidly reconfigurable, high-fidelity optical arbitrary waveform generation (OAWG) in a heterogeneous photonic integrated circuit (PIC). The heterogeneous PIC combines advantages of high-speed indium phosphide (InP) modulators and low-loss, high-contrast silicon nitride (Si₃N₄) arrayed waveguide gratings (AWGs) so that high-fidelity optical waveform syntheses with rapid waveform updates are possible. The generated optical waveforms spanned a 160 GHz spectral bandwidth starting from an optical frequency comb consisting of eight comb lines separated by 20 GHz channel spacing. The Error Vector Magnitude (EVM) values of the generated waveforms were approximately 16.4%. The OAWG module can rapidly and arbitrarily reconfigure waveforms upon every pulse arriving at 2 ns repetition time. The result of this work indicates the feasibility of truly dynamic optical arbitrary waveform generation where the reconfiguration rate or the modulator bandwidth must exceed the channel spacing of the AWG and the optical frequency comb.

Tunable delay control of entangled photons based on dispersion cancellation

We propose and demonstrate a novel approach for controlling the temporal position of the biphoton correlation function using pump frequency tuning and dispersion cancellation; precise waveguide engineering enables biphoton generation at different pump frequencies while the idea of nonlocal dispersion cancellation is used to create the relative signal-idler delay and simultaneously prevents broadening of their correlation. Experimental results for delay shifts up to ±15 times the correlation width are shown along with discussions of the performance metrics of this approach.

Bi-photon spectral correlation measurements from a silicon nanowire in the quantum and classical regimes

The growing requirement for photon pairs with specific spectral correlations in quantum optics experiments has created a demand for fast, high resolution and accurate source characterisation. A promising tool for such characterisation uses classical stimulated processes, in which an additional seed laser stimulates photon generation yielding much higher count rates, as recently demonstrated for a χ(2) integrated source in A. Eckstein et al. Laser Photon. Rev. 8, L76 (2014). In this work we extend these results to χ(3) integrated sources, directly measuring for the first time the relation between spectral correlation measurements via stimulated and spontaneous four wave mixing in an integrated optical waveguide, a silicon nanowire. We directly confirm the speed-up due to higher count rates and demonstrate that this allows additional resolution to be gained when compared to traditional coincidence measurements without any increase in measurement time. As the pump pulse duration can influence the degree of spectral correlation, all of our measurements are taken for two different pump pulse widths. This allows us to confirm that the classical stimulated process correctly captures the degree of spectral correlation regardless of pump pulse duration, and cements its place as an essential characterisation method for the development of future quantum integrated devices.

Quantum optical arbitrary waveform manipulation and measurement in real time

We describe a technique for dynamic quantum optical arbitrary-waveform generation and manipulation, which is capable of mode selectively operating on quantum signals without inducing significant loss or decoherence. It is built upon combining the developed tools of quantum frequency conversion and optical arbitrary waveform generation. Considering realistic parameters, we propose and analyze applications such as programmable reshaping of picosecond-scale temporal modes, selective frequency conversion of any one or superposition of those modes, and mode-resolved photon counting. We also report on experimental progress to distinguish two overlapping, orthogonal temporal modes, demonstrating over 8 dB extinction between picosecond-scale time-frequency modes, which agrees well with our theory. Our theoretical and experimental progress, as a whole, points to an enabling optical technique for various applications such as ultradense quantum coding, unity-efficiency cavity-atom quantum memories, and high-speed quantum computing.

Ultrafast time-division demultiplexing of polarization-entangled photons

Maximizing the information transmission rate through quantum channels is essential for practical implementation of quantum communication. Time-division multiplexing is an approach for which the ultimate rate requires the ability to manipulate and detect single photons on ultrafast time scales while preserving their quantum correlations. Here we demonstrate the demultiplexing of a train of pulsed single photons using time-to-frequency conversion while preserving their polarization entanglement with a partner photon. Our technique converts a pulse train with 2.69 ps spacing to a frequency comb with 307 GHz spacing which may be resolved using diffraction techniques. Our work enables ultrafast multiplexing of quantum information with commercially available single-photon detectors.