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arXiv:1709.05826 · Physical Review A

Interferometric modulation of quantum cascade interactions

Stefano Cusumano, Andrea Mari, Vittorio Giovannetti

Published May 10, 2018• 13 citations
arXivHTMLPDF

Abstract

We consider many-body quantum systems dissipatively coupled by a cascade network, i.e., a setup in which interactions are mediated by unidirectional environmental modes propagating through a linear optical interferometer. In particular we are interested in the possibility of inducing different effective interactions by properly engineering an external dissipative network of beam splitters and phase shifters. In this work we first derive the general structure of the master equation for a symmetric class of translation-invariant cascade networks. Then we show how, by tuning the parameters of the interferometer, one can exploit interference effects to tailor a large variety of many-body interactions.

DOI
10.1103/physreva.97.053811

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We consider many-body quantum systems dissipatively coupled by a cascade network, i.e., a setup in which interactions are mediated by unidirectional environmental modes propagating through a linear optical interferometer. In particular we are interested in the possibility of inducing different effective interactions by properly engineering an external dissipative network of beam splitters and phase shifters. In this work we first derive the general structure of the master equation for a symmetric class of translation-invariant cascade networks. Then we show how, by tuning the parameters of the interferometer, one can exploit interference effects to tailor a large variety of many-body interactions.
In this work we consider quantum cascade networks in which quantum systems are connected through unidirectional channels that can mutually interact giving rise to interference effects. In particular we show how to compute master equations for cascade systems in an arbitrary interferometric configuration by means of a collisional model. We apply our general theory to two specific examples: the first consists of two systems arranged in a Mach-Zender-like configuration and the second is a three system network where it is possible to tune the effective chiral interactions between the nodes exploiting interference effects.
We study the dissipative dynamics and the formation of entangled states in driven cascaded quantum networks, where multiple systems are coupled to a common unidirectional bath. Specifically, we identify the conditions under which emission and coherent reabsorption of radiation drives the whole network into a pure stationary state with non-trivial quantum correlations between the individual nodes. We illustrate this effect in more detail for the example of cascaded two-level systems, where we present an explicit preparation scheme that allows one to tune the whole network through 'bright' and 'dark' states associated with different multi-partite entanglement patterns. In a complementary setting consisting of cascaded nonlinear cavities, we find that two cavity modes can be driven into a non-Gaussian entangled dark state. Potential realizations of such cascaded networks with optical and microwave photons are discussed.
This paper presents a realization algorithm for a class of complex transfer functions corresponding to physically realizable complex linear quantum systems. The class of complex linear quantum systems under consideration includes interconnections of passive optical components such as cavities, beam-splitters, phase-shifters and interferometers. It is shown that for almost all quantum optical systems within this class, the corresponding transfer function can be realized as a cascade connection involving only cavities and phase-shifters.
Photonic quantum computing is a strong contender in the race to fault-tolerance. Recent proposals using qubits encoded in frequency modes promise a large reduction in hardware footprint, and have garnered much attention. In this encoding, linear optics, i.e., beam splitters and phase shifters, is necessarily not energy-conserving, and is costly to implement. In this work, we present designs of frequency-mode beam splitters based on modulated arrays of coupled resonators. We develop a methodology to construct their effective transfer matrices based on the SLH formalism for quantum input-output networks. Our methodology is flexible and highly composable, allowing us to define NNN-mode beam splitters either natively based on arrays of NNN-resonators of arbitrary connectivity or as networks of interconnected lll-mode beam splitters, with l<Nl<Nl<N. We apply our methodology to analyze a two-resonator device, a frequency-domain phase shifter and a Mach-Zehnder interferometer obtained from composing these devices, a four-resonator device, and present a formal no-go theorem on the possibility of natively generating certain NNN-mode frequency-domain beam splitters with arrays of NNN-resonators.