Dileep V. Reddy

Photon Temporal Modes: A Complete Framework for Quantum Information Science

Field-orthogonal temporal modes of photonic quantum states provide a new framework for quantum information science (QIS). They intrinsically span a high-dimensional Hilbert space and lend themselves to integration into existing single-mode fiber communication networks. We show that the three main requirements to construct a valid framework for QIS -- the controlled generation of resource states, the targeted and highly efficient manipulation of temporal modes and their efficient detection -- can be fulfilled with current technology. We suggest implementations of diverse QIS applications based on this complete set of building blocks.

Temporal mode selectivity by frequency conversion in second-order nonlinear optical waveguides

We explore theoretically the feasibility of using frequency conversion by sum- or difference-frequency generation, enabled by three-wave-mixing, for selectively multiplexing orthogonal input waveforms that overlap in time and frequency. Such a process would enable a drop device for use in a transparent optical network using temporally orthogonal waveforms to encode different channels. We model the process using coupled-mode equations appropriate for wave mixing in a uniform second-order nonlinear optical medium pumped by a strong laser pulse. We find Green functions describing the process, and employ Schmidt (singular-value) decompositions thereof to quantify its viability in functioning as a coherent waveform discriminator. We define a selectivity figure of merit in terms of the Schmidt coefficients, and use it to compare and contrast various parameter regimes via extensive numerical computations. We identify the most favorable regime (at least in the case of no pump chirp) and derive the complete analytical solution for the same. We bound the maximum achievable selectivity in this parameter space. We show that including a frequency chirp in the pump does not improve selectivity in this optimal regime. We also find an operating regime in which high-efficiency frequency conversion without temporal-shape selectivity can be achieved while preserving the shapes of a wide class of input pulses. The results are applicable to both classical and quantum frequency conversion.

Efficient sorting of quantum-optical wave packets by temporal-mode interferometry

Long-distance quantum communication relies on storing and retrieving photonic qubits in orthogonal field modes. The available degrees of freedom for photons are polarization, spatial-mode profile, and temporal/spectral profile. To date, methods exist for decomposing, manipulating, and analyzing photons into orthogonal polarization modes and spatial modes. Here we propose and theoretically verify the first highly efficient method to carry out analogous operations for temporally and spectrally overlapping, but field-orthogonal, temporal modes. The method relies on cascaded nonlinear-optical quantum frequency conversion.

Sorting photon wave packets using temporal-mode interferometry based on multiple-stage quantum frequency conversion

All classical and quantum technologies that encode in and retrieve information from optical fields rely on the ability to selectively manipulate orthogonal field modes of light. Such manipulation can be achieved with high selectivity for polarization modes and transverse-spatial modes. For the time-frequency degree of freedom, this could efficiently be achieved for a limited choice of approximately orthogonal modes, i.e. non-overlapping bins in time or frequency. We recently proposed a method that surmounts the selectivity barrier for sorting arbitrary orthogonal temporal modes [Opt. Lett. {\bf 39}, 2924 (2014)] using cascaded interferometric quantum frequency conversion in nonlinear optical media. We call this method temporal-mode interferometry, as it has a close resemblance to the well-known separated-fields atomic interferometry method introduced by Ramsey. The method has important implications for quantum memories, quantum dense coding, quantum teleportation, and quantum key distribution. Here we explore the inner workings of the method in detail, and extend it to multiple stages with a concurrent asymptotic convergence of temporal-mode selectivity to unity. We also complete our analysis of pump-chirp compensation to counter pump-induced nonlinear phase-modulation in four-wave mixing implementations.

Engineering temporal-mode-selective frequency conversion in nonlinear optical waveguides: from theory to experiment

Quantum frequency conversion (FC) in nonlinear optical media is a powerful tool for temporal-mode selective manipulation of light. Recent attempts at achieving high mode selectivities and/or fidelities have had to resort to multi-dimensional optimization schemes to determine the systems natural Schmidt modes. Certain combinations of relative-group velocities between the relevant frequency bands, medium length, and temporal pulse widths have been known to achieve good selectivities (exceeding 80%) for temporal modes that are nearly identical to pump pulse shapes, even for high conversion efficiencies. Working in this parameter regime using an off-the-shelf, second-harmonic generation, MgO:PPLN waveguide, and with pulses on the order of 500 fs at wavelengths around 800 nm, we verify experimentally that model-predicted Schmidt modes provide the high temporal-mode selectivity expected. The good agreement between experiment and theory paves the way to the implementation of a proposed two-stage FC scheme that is predicted by the present theory to reach near-perfect (100%) selectivity.

Observation of Interaction of Spin and Intrinsic Orbital Angular Momentum of Light

The interaction of spin and intrinsic orbital angular momentum of light is observed, as evidenced by length-dependent rotations of both spatial patterns and optical polarization in a cylindrically symmetric isotropic optical fiber. Such rotations occur in a straight few-mode fiber when superpositions of two modes with parallel and antiparallel orientation of spin and intrinsic orbital angular momentum (IOAM=2ℏ) are excited, resulting from a degeneracy splitting of the propagation constants of the modes.

Theory of noise suppression in Λ -type quantum memories by means of a cavity

Quantum memories, capable of storing single photons or other quantum states of light, to be retrieved on demand, offer a route to large-scale quantum information processing with light. A promising class of memories is based on far-off-resonant Raman absorption in ensembles of Λ-type atoms. However, at room temperature these systems exhibit unwanted four-wave mixing, which is prohibitive for applications at the single-photon level. Here, we show how this noise can be suppressed by placing the storage medium inside a moderate-finesse optical cavity, thereby removing the main roadblock hindering this approach to quantum memory.

Double-heralded generation of two-photon-states by spontaneous four-wave-mixing in the presence of noise.

We present an experimental method for creating and verifying photon-number states created by non-degenerate, third-order nonlinear-optical photon-pair sources. By using spatially multiplexed, thresholding single-photon detectors and inverting a conditional probability matrix, we determine the photon-number probabilities created through heralded spontaneous four-wave-mixing. The deleterious effects of noise photons on reliable heralding are investigated and shown to degrade the conditional preparation of two-photon number states more than they degrade conditional single-photon states. We derive the equivalence between the presence of unwanted noise in the herald channel and loss in the signal channel of heralded experiments. A procedure for characterizing the noise-photon contributions, and a means of estimating the herald noise-free photon-number distribution is demonstrated.

Time reversal of arbitrary photonic temporal modes via nonlinear optical frequency conversion

Single-photon wave packets can carry quantum information between nodes of a quantum network. An important general operation in photon-based quantum information systems is blind reversal of a photons temporal wave-packet envelope, that is, the ability to reverse an envelope without knowing the temporal state of the photon. We present an all-optical means for doing so, using nonlinear-optical frequency conversion driven by a short pump pulse. This scheme allows for quantum operations such as a temporal-mode parity sorter. We also verify that the scheme works for arbitrary states (not only single-photon ones) of an unknown wave packet.

Temporal mode selectivity by frequency conversion in second-order nonlinear optical waveguides: Erratum (Optics Express (2013) 21 (13840-13863) DOI: 10.1364/OE.21.013840)

We correct typographical errors in four equations showing the integral forms of the equations of motion and the corresponding perturbative approximation. Subsequently presented derivations, results, and conclusions remain unchanged.