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arXiv:2103.04022 · Journal of the Optical Society of America B

Quantum state preparation and one qubit logic from third-order nonlinear interactions

Francisco A. Domínguez-Serna, Karina Garay-Palmett

Published Jun 22, 2021• 2 citations
arXivHTMLPDF

Abstract

We present a study on preparing and manipulating temporal-mode (TM) qubits based on third-order nonlinear interactions. Specifically, we consider the process of frequency conversion via difference frequency generation. To prepare a qubit, we aim to use Gaussian input states to a nonlinear waveguide. The coupling between the input state and a specific TM is maximized, obtaining qubits prepared with fidelities close to one. TMs evolve linearly within the medium; therefore, it is possible to define rotations around any axis contained in the x y plane, allowing spanning the full Bloch sphere in two steps. Particularly, we present a method to obtain any of the Pauli quantum gates by varying geometric or user-accessible parameters in a given experimental configuration when time-ordering effects are ignored. Our study allows for experimentally feasible proposals capable of controllable arbitrary qubit transformations.

DOI
10.1364/josab.424374

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We present a study on preparing and manipulating temporal-mode (TM) qubits based on third-order nonlinear interactions. Specifically, we consider the process of frequency conversion via difference frequency generation. To prepare a qubit, we aim to use Gaussian input states to a nonlinear waveguide. The coupling between the input state and a specific TM is maximized, obtaining qubits prepared with fidelities close to one. TMs evolve linearly within the medium; therefore, it is possible to define rotations around any axis contained in the x y plane, allowing spanning the full Bloch sphere in two steps. Particularly, we present a method to obtain any of the Pauli quantum gates by varying geometric or user-accessible parameters in a given experimental configuration when time-ordering effects are ignored. Our study allows for experimentally feasible proposals capable of controllable arbitrary qubit transformations.
We present a novel proposal for the implementation of temporal-modes quantum gates based on the third-order nonlinear process of difference frequency generation in an integrated photonic circuit, which allows switching from one Pauli gate to another by tuning the phase difference between the two pump pulses (in case of the σx\sigma_{x}σx​ and σy\sigma_{y}σy​ Pauli gates) and between the two states comprising the basis of single temporal-modes qubits (in the case of the σz\sigma_{z}σz​ Pauli gate). We demonstrate that our proposal enables the preparation of any single temporal-mode qubit and rotations on the Bloch sphere by changing externally controllable parameters. We also analyze the effects of fabrication errors on the predicted quantum gate fidelity, finding that even if some waveguide parameter deviates from the design, slight tuning of pump wavelengths can lead to recovering high fidelity values.
This work presents a feasible design of an integrated photonic circuit performing as a device for single-qubit preparation and rotations through the third-order nonlinear process of difference frequency generation (DFG) and defined in the temporal mode basis. The first stage of our circuit includes the generation of heralded single photons by spontaneous four-wave mixing in a micro-ring cavity engineered for delivering a single-photon state in a unique temporal mode. The second stage comprises the implementation of DFG in a spiral waveguide with controlled dispersion properties for reaching color qubit preparation fidelity close to unity. We present the generalized rotation operator related to the DFG process, a methodology for the device design, and qubit preparation fidelity results as a function of user-accessible parameters.
The temporal-mode (TM) basis is a prime candidate to perform high-dimensional quantum encoding. Quantum frequency conversion has been employed as a tool to perform tomographic analysis and manipulation of ultrafast states of quantum light necessary to implement a TM-based encoding protocol. While demultiplexing of such states of light has been demonstrated in the quantum pulse gate (QPG), a multiplexing device is needed to complete an experimental framework for TM encoding. In this work we demonstrate the reverse process of the QPG. A dispersion-engineered difference frequency generation in nonlinear optical waveguides is employed to imprint the pulse shape of the pump pulse onto the output. We study experimentally the process by spectrally shaping the first five orders of Hermite-Gauss modes of various bandwidths. Finally, we establish and model the limits of practical, reliable spectral pulse shaping operation.
Full control over the spatiotemporal structure of quantum states of light is an important goal in quantum optics, to generate, for instance, single-mode quantum pulses or to encode information on multiple modes, enhancing channel capacities. Quantum light pulses feature an inherent, rich spectral broadband-mode structure. In recent years, exploring the use of integrated optics as well as source engineering has led to a deep understanding of the pulse-mode structure of guided quantum states of light. In addition, several groups have started to investigate the manipulation of quantum states by means of single-photon frequency conversion. In this paper, we explore new routes towards complete control of the inherent pulse-modes of ultrafast pulsed quantum states by employing specifically designed nonlinear waveguides with adapted dispersion properties. Starting from our recently proposed quantum pulse gate (QPG), we further generalize the concept of spatiospectral engineering for arbitrary χ (2) -based quantum processes. We analyse the sum-frequency generation-based QPG and introduce the difference-frequency generation-based quantum pulse shaper (QPS). Together, these versatile and robust integrated optical devices allow for arbitrary manipulations of the pulse-mode structure of ultrafast pulsed quantum states. The QPG can be utilized to select an arbitrary pulse mode from a multimode input state, whereas the QPS enables the generation of specific pulse modes from an input wavepacket with a Gaussian-shaped spectrum.
We generalize our previous results of universal linear manipulations [Phys. Rev. A 63, 032304 (2001)] to investigate three types of nonlinear qubit transformations using measurement and quantum-based schemes. First, nonlinear rotations are studied. We rotate different parts of a Bloch sphere in opposite directions about the z axis. The second transformation is a map that sends a qubit to its orthogonal state. We consider the case in which the orthogonal state is applied to only a partial area of a Bloch sphere. We also study nonlinear general transformation, i.e., $(\ensuremath{\vartheta},\ensuremath{\varphi})\ensuremath{\rightarrow}(\ensuremath{\vartheta}\ensuremath{-}\ensuremath{\alpha},\ensuremath{\varphi}),$ again applied only to part of the Bloch sphere. In order to achieve these three operations, we consider different measurement preparations and derive the optimal average (instead of universal) quantum unitary transformations. We also introduce a simple method for a qubit measurement and its application to other cases.