Quantum Optics

During my PhD research in MIT Optical and Quantum Communication Group, I work on architecture for long-distance quantum communication relies on fiber-optic transmission of polarization-entangled photons from a dual parametric amplifier source to a pair of trapped Rb atom quantum memories. The protocol requires a high-flux continuous-wave source of polarization-entangled photons at 795 nm and 1.55 mm, for the loading of local and remote quantum memories, respectively. Out of each pair of entangled photons produced by the source, one of the photons is sent to Alice’s local station while the conjugate photon travels over standard telecommunication fiber to Bob’s remote receiver node. In order to load the remotely-located memory, quantum-state frequency conversion is required, so that the polarization state of the 1.55 mm photon is transferred to a 795 nm photon. This form of frequency upconversion must function down to the single photon level with low insertion loss, while providing both high conversion efficiency and high-fidelity preservation of arbitrary polarization states. Surrounding quantum optical system and quantum communication, I worked on following topics:

(1) Parametric down conversion for single-photon generation.

(2) Quantum cryptography.

(3) Quantum computation with second-order photon interaction.

Parametric down conversion for single photon generation

Nonclassical states of light, such as single-photon states, polarization-entangled states and multi-photon path-entangled states are essential for linear-optical quantum computation, quantum communication, quantum metrology, and experimental tests of quantum foundations. Spontaneous parametric down-conversion (SPDC) employing the χ (2) nonlinearity is a standard tool for generating nonclassical light.

Fig. 1. Schematics of experiment setups. (a) SPDC photon pairs generation and collection. Pump spectrum is controlled using a pair of diffraction gratings (DGs) in a 4 f optical configuration. (b) Single-fiber spectrometer with counter-propagating signal and idler and coincidence detection by SNSPDs D1 and D2. (c) DCM spectrometer providing high resolution JSI measurements. A, rectangular aperture; L1, f = 20 cm lens; L2, f = 40 cm lens; L3, f = 10 cm lens; LPF, long-pass filter; PBS, polarization beam splitter.

I designed a scheme based on periodic polling of nonlinear crystal (Fig. 1) to prepare single-photon sources that established a new record for photon-purity. This photon source was adopted to demonstrate cryptography protocols and machine learning applications in nonlinear-optical systems. Also at MIT, I resolved a longstanding open problem regarding the security of finite-key distribution based on time-energy entanglement, which was implemented by MIT Lincoln Laboratory and is still one of the most efficient quantum key distribution schemes available to date.

Parametric down conversion for Fock state generation

Fig. 2. 3D plot showing the UPDC procedure in the two-pump-photon subspace that realizes unity-efficiency conversion from the |0, 0, 2> input state, shown as the blue dot, to the |2, 2, 0> final state, shown as the red dot, in a single Grover iteration. The UPDC procedure’s initial state, prepared by passing the input state through a type-II phase-matched χ (2) crystal for an interaction time, is shown by the purple dot that is obtained by evolution around the red circle from the blue dot. Sign flip on the marked state (|0, 0, 2>) transforms the initial state to a new state, which is indicated by the green dot. Rotation toward the marked state by passing this new state through a type-II phase-matched χ (2) crystal for an interaction time designed according to interaction strength of the crystal leads to the desired output state |2, 2, 0>.

The limitation on the purity and efficiency of parametric down conversion on generating Fock State is more fundamental: the exact dynamics of three-wave mixing predicts that the down-conversion efficiency will not be unity for Fock state |n> where n>1 due to the characteristics of the three-wave mixing Hamiltonian energy spectrum. In a work published in Physical Review Letter, we utilize a quantum algorithm: Grover search, to overcome this innate limitation of quantum optics, we propose an optical scheme, employing optical parametric down-converters interlaced with nonlinear sign gates, that completely converts an n-photon Fock-state pump to n signal-idler photon pairs when the down-converters’ crystal lengths are chosen appropriately, see Fig. 2.

Quantum cryptography

Time-energy high-dimensional quantum key distribution (HD-QKD) leverages the high-dimensional nature of time-energy entangled biphotons and the loss tolerance of single-photon detection to achieve long-distance key distribution with high photon information efficiency. The general-attack security of HD-QKD had only been proven in the asymptotic regime, while HD-QKD’s finite-key security has only been established for a limited set of attacks.

I filled this gap by providing a rigorous HD-QKD security proof for general attacks in the finite-key regime. Our proof relied on a novel entropic uncertainty relation that we derive for time and conjugate-time measurements using dispersive optics, and our analysis included an efficient decoy-state protocol in its parameter estimation.

Our cryptography protocol was implemented by MIT Lincoln Laboratory and is still one of the most efficient quantum key distribution schemes available to date.

Quantum computation with second-order photon interaction.

Nonlinear optical systems are considered not promising for scalable quantum computation due to the prevalent photon loss in the system. Previous methods to protect against photon loss for photonic computation are too inefficient to be feasible in experiment. Address these realistic concerns, I proposed a new framework for quantum error correction that exploits the inherent symmetries in the physical substrate underlying a given quantum device.

In Qudit-Basis Universal Quantum Computation Using χ ( 2 ) Interactions we prove that universal quantum computation can be realized—using only linear optics and χ ( 2 ) (three-wave mixing) interactions—in any ( n + 1 )-dimensional qudit basis of the n -pump-photon subspace. First, we exhibit a strictly universal gate set for the qubit basis in the one-pump-photon subspace. Next, we demonstrate qutrit-basis universality by proving that χ ( 2 ) Hamiltonians and photon-number operators generate the full u ( 3 ) Lie algebra in the two-pump-photon subspace, and showing how the qutrit controlled- Z gate can be implemented with only linear optics and χ ( 2 ) interactions. We then use proof by induction to obtain our general qudit result. Our induction proof relies on coherent photon injection or subtraction, a technique enabled by χ ( 2 ) interaction between the encoding modes and ancillary modes. Finally, we show that coherent photon injection is more than a conceptual tool, in that it offers a route to preparing high-photon-number Fock states from single-photon Fock states.