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arXiv:2003.10673 · Physical Review A

Analytic and geometric properties of scattering from periodically modulated quantum-optical systems

Rahul Trivedi, Alexander D. White, Shanhui Fan, Jelena Vuckovic A

Published Sep 8, 2020• 10 citations
arXivHTMLPDF

Abstract

We study the scattering of photons from periodically modulated quantum-optical systems. For excitation-number-conserving quantum-optical systems, we connect the analytic structure of the frequency-domain $N$-photon scattering matrix of the system to the Floquet decomposition of its effective Hamiltonian. Furthermore, it is shown that the first-order contribution to the transmission or equal-time $N$-photon correlation spectrum with respect to the modulation frequency is completely geometric in nature, i.e., it depends only on the Hamiltonian trajectory and not on the precise nature of the modulation being applied.

DOI
10.1103/physreva.102.033707

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We study the scattering of photons from periodically modulated quantum-optical systems. For excitation-number-conserving quantum-optical systems, we connect the analytic structure of the frequency-domain NNN-photon scattering matrix of the system to the Floquet decomposition of its effective Hamiltonian. Furthermore, it is shown that the first-order contribution to the transmission or equal-time NNN-photon correlation spectrum with respect to the modulation frequency is completely geometric in nature, i.e., it depends only on the Hamiltonian trajectory and not on the precise nature of the modulation being applied.
The dynamical control of single-photon scattering in a one-dimensional waveguide coupled to a Floquet atom-cavity system with time-modulated coupling constants is investigated. The analytical expressions for determining the scattering properties are obtained by using an effective Floquet Hamiltonian in real space. The photon transport is extremely sensitive to the time-modulated atom-cavity coupling strengths. Two cases, i.e., the effective Floquet Hamiltonian either includes or excludes a static coupling term, are discussed in detail. The results show that, with such Floquet atom-cavity configuration, an active photonic switch with nearly ideal switching contrast could be implemented. The transmission of the waveguide photons with different frequencies can dynamically be switched on or off via adjusting the modulated amplitude or relative modulated phase no matter whether the static coupling between the atom and the two cavity modes is considered or not. The application of the dynamic modulated atom-cavity coupling strengths instead of a purely static one makes our photonic switch more tunable. These results are expected to be applicable in quantum information processing and in active quantum device design involving dynamical modulation.
We consider a quantum system periodically driven with a strength which varies slowly on the scale of the driving period. The analysis is based on a general formulation of the Floquet theory relying on the extended Hilbert space. It is shown that the dynamics of the system can be described in terms of a slowly varying effective Floquet Hamiltonian that captures the long-term evolution, as well as rapidly oscillating micromotion operators. We obtain a systematic high-frequency expansion of all these operators. Generalizing the previous studies, the expanded effective Hamiltonian is now time dependent and contains extra terms appearing due to changes in the periodic driving. The same applies to the micromotion operators which exhibit a slow temporal dependence in addition to the rapid oscillations. As an illustration, we consider a quantum-mechanical spin in an oscillating magnetic field with a slowly changing direction. The effective evolution of the spin is then associated with non-Abelian geometric phases reflecting the geometry of the extended Floquet space. The developed formalism is general and also applies to other periodically driven systems, such as shaken optical lattices with a time-dependent shaking strength, a situation relevant to the cold-atom experiments.
Quantum systems can show qualitatively new forms of behavior when they are driven by fast time-periodic modulations. In the limit of large driving frequency, the long-time dynamics of such systems can often be described by a time-independent effective Hamiltonian, which is generally identified through a perturbative treatment. Here, we present a general formalism that describes time-modulated physical systems, in which the driving frequency is large, but resonant with respect to energy spacings inherent to the system at rest. Such a situation is currently exploited in optical-lattice setups, where superlattice (or Wannier-Stark-ladder) potentials are resonantly modulated so as to control the tunneling matrix elements between lattice sites, offering a powerful method to generate artificial fluxes for cold-atom systems. The formalism developed in this work identifies the basic ingredients needed to generate interesting flux patterns and band structures using resonant modulations. Additionally, our approach allows for a simple description of the micromotion underlying the dynamics; we illustrate its characteristics based on diverse dynamic-lattice configurations. It is shown that the impact of the micromotion on physical observables strongly depends on the implemented scheme, suggesting that a theoretical description in terms of the effective Hamiltonian alone is generally not sufficient to capture the full time evolution of the system.
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An optical chopper periodically interrupts a classical light beam. We propose a realizable quantum version of the optical chopper, where the time-periodic driving of the light-matter coupling is achieved through a nonlinear three wave mixing element. We theoretically investigate how our scheme can be used for the controllable shaping of few photon light. Using Floquet dynamics, we find strong periodic modulations of the transmission and reflection envelopes in the scattered few-photon pulses, including photon compression and blockade, as well as dramatic changes in the quantum light statistics. Our theoretical analysis allows us to explain these non-trivial phenomena as arising from non-adiabatic memory effects.
Abstract The dynamics of qubits coupled to a harmonic oscillator with time-periodic coupling is investigated in the framework of Floquet theory. This system can be used to model nonadiabatic phenomena that require a periodic modulation of the qubit/oscillator coupling. The case of a single qubit coupled to a resonator populated with n = 0, 1 photon is explicitly treated. The time-dependent Schrödinger equation describing the system’s dynamics is solved within the Floquet formalism and compared to a solution obtained with perturbative approaches in the time- and Laplace-domain. Excellent quantitative agreement is found between the analytical and numerical calculations within the Floquet approach, demonstrating the effectiveness of the technique for the study of the dynamical Lamb effect.