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arXiv:2204.11377 · Physical Review A

Quantum state transfer and input-output theory with time reversal

Kevin Randles, S. J. van Enk

Published Jul 19, 2023• 3 citations
arXivHTMLPDF

Abstract

Being able to reliably transfer the quantum state from one system to another is crucial to developing quantum networks. A standard way to accomplish this transfer of information is by making use of an intermediate information carrier (e.g., a photon) that is emitted by the first system and absorbed by the second. For such a scenario one can develop an effective description by eliminating the intermediate degrees of freedom, which yields an effective direct coupling between the two systems. If, however, the spectral properties of the two systems are different, the photon's time-frequency shape needs to be appropriately modified before it reaches the second system. We study here the effective description that results when we thus manipulate the intermediate photon. We examine a unitary transformation $U$ that time reverses, frequency translates, and stretches the photon wave packet. We find that the concomitant modifications to the effective description can best be understood in terms of a change to the state's time argument $\ensuremath{\rho}(t)={\ensuremath{\rho}}_{1}(\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{t})\ensuremath{\bigotimes}{\ensuremath{\rho}}_{2}(t)$, where $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{t}$ is a fictitious time for the first system that is stretched and runs backward. We apply this theory to three-level $\mathrm{\ensuremath{\Lambda}}$ systems inside optical cavities, and we numerically illustrate how performing the unitary transformation $U$ results in improved quantum state transfer.

DOI
10.1103/physreva.108.012421

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Being able to reliably transfer the quantum state from one system to another is crucial to developing quantum networks. A standard way to accomplish this transfer of information is by making use of an intermediate information carrier (e.g., a photon) that is emitted by the first system and absorbed by the second. For such a scenario one can develop an effective description by eliminating the intermediate degrees of freedom, which yields an effective direct coupling between the two systems. If, however, the spectral properties of the two systems are different, the photon's time-frequency shape needs to be appropriately modified before it reaches the second system. We study here the effective description that results when we thus manipulate the intermediate photon. We examine a unitary transformation UUU that time reverses, frequency translates, and stretches the photon wave packet. We find that the concomitant modifications to the effective description can best be understood in terms of a change to the state's time argument \ensuremathρ(t)=\ensuremathρ1(t\ifmmode~\else˜\fi)\ensuremath⨂\ensuremathρ2(t)\ensuremath{\rho}(t)={\ensuremath{\rho}}_{1}(\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{t})\ensuremath{\bigotimes}{\ensuremath{\rho}}_{2}(t)\ensuremathρ(t)=\ensuremathρ1​(t\ifmmode~\else˜\fi​)\ensuremath⨂\ensuremathρ2​(t), where t\ifmmode~\else˜\fi\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{t}t\ifmmode~\else˜\fi​ is a fictitious time for the first system that is stretched and runs backward. We apply this theory to three-level \ensuremathΛ\mathrm{\ensuremath{\Lambda}}\ensuremathΛ systems inside optical cavities, and we numerically illustrate how performing the unitary transformation UUU results in improved quantum state transfer.
We develop quantum-optical input-output theory for resonators with arbitrary coupling strength, and for input fields whose spectrum can be wider than the cavity free-spectral range, while ensuring that the field-operator commutator relations in space-time variables are correct. The cavity-field commutator exhibits a series of space-time ``echoes,'' representing causal connections of certain space-time points by light propagation. We apply the theory to two-photon wave-packet shaping by cavity reflection, which displays a remarkable illustration of dispersion cancellation. We also show that the theory is amenable to inclusion of intracavity absorbing and emitting atoms, allowing, for example, dissipative losses within the cavity to be incorporated in a quantum mechanically correct way.
For the realization of a quantum network and efficient transfer of information between its nodes, many challenges should be resolved. One of these challenges is related to controlling photons, in that receiving and resending data in a real-time process should be reliable. The uncontrollable and time asymmetry shape of the photon wave packets emitted by quantum sources creates obstacles for reliable information transfer. In this work, an approach has been introduced to tune the wave packet shape of a single photon as a significant factor for absorbing and resending the same information. Since the wave packet of the photon emitted from spontaneous emission cannot be handled, in this research for the wave packet shaping, two lasers with a phase difference between them are proposed, where Rabi frequency Ω ( t ) is considered as a time-dependent function. Studying the temporal evolution of the system states and using the experimental parameters of a real single photon are two steps employed in this paper to achieve the desired outcome. Furthermore, the fidelity of two distant nodes, between which information is transmitted by the proposed single photon, is examined.
We consider two memory nodes of a quantum network connected by flying qubits. We are particularly interested in the case where a flying qubit produced by one node has to be transformed before it can interface efficiently with the next node. Such transformations can be utilized as a key part of the distribution of quantum states and hence entanglement between the nodes of a hybrid quantum network linking together different quantum technologies. We show how and why the probability of interfacing successfully is determined by the overlap of the spectral shape of the actual flying qubit and the ideal shape. This allows us to analytically and numerically analyze how the probability of success is impacted by realistic errors, and show the utility of our scheme (in consonance with known error correction methods) in connecting hybrid nodes of a quantum network. We focus here on a concrete implementation in which the memory nodes consist of three-level atoms in cavities and the flying qubits are photons.
The controlled transfer of quantum entangled states is a fascinating topic in quantum physics, and has potential applications in fields such as quantum network communication, distributed quantum information processing, and development of quantum functional devices. This study focuses on a circuit quantum electrodynamics (QED) system, comprising an input port, two output ports, and a quantum switch. The input port or each output port contains n microwave cavities. The switch is a superconducting transmon qutrit (three-level quantum system). The vacuum and single-photon states in each cavity encode a photonic qubit. We demonstrate that the single-excitation symmetric (SES) entangled state of n photonic qubits can be transferred from the n cavities at the input port to the n cavities at either of the two output ports, controlled by the switch. Remarkably, the operational time decreases as the number n increases. The only use of qutrit-cavity resonant interaction enables rapid quantum state transfer while effectively suppressing system decoherence. This proposal can be used to achieve the controlled transfer of both Bell states and W states of photonic qubits via a quantum switch. To validate the experimental feasibility, we numerically simulate two scenarios: (i) transferring the Bell state of two photonic qubits, and (ii) transferring the W state of three photonic qubits. This proposal may be extended to accomplish the same task in other physical systems, where the switch is implemented with a three-level artificial atom of different types while each cavity is a microwave or optical cavity.
Abstract A method is presented for transfer of a quantum state from one atom to another atom. In this method, we consider the interaction of a multi-mode cavity with a multi-level quantum system and adopt the multi-photon resonance theory for preparing an efficient quantum memory and a quantum network. From the use of effective two- and three-level Hamiltonians, the proper values for interaction times, coupling constants, and detunings are predicted. To examine the sensitivity of the quantum state transfer against decoherence processes, we introduce the quantum-jump approach. Proceeding with this approach leads to a description of the system via wavefunctions instead of density operators and provides simple effective differential equations for obtaining analytic expressions of the probability amplitudes.
High-fidelity state transfer is fundamentally limited by time-reversal symmetry: one qubit emits a photon with a certain temporal pulse shape, whereas a second qubit requires the time-reversed pulse shape to efficiently absorb this photon. This limit is often overcome by introducing active elements. Here, we propose an alternative solution: by tailoring the dispersion relation of a waveguide, the photon pulse emitted by one qubit is passively reshaped into its time-reversed counterpart, thus enabling perfect absorption. We analytically derive the optimal dispersion relations in the limit of small and large qubit-qubit separations, and numerically extend our results to arbitrary separations via multiparameter optimization. We further propose a spatially inhomogeneous waveguide that renders the state transfer robust to variations in qubit separations. In all cases, we obtain near-unity transfer fidelity (>= 98%) that is robust against imperfections in parameter values and propagation loss. Our dispersion-engineered waveguide provides a compact and passive route toward on-chip quantum networks, highlighting dispersion as a powerful resource in waveguide quantum electrodynamics.