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arXiv:1602.08009 · Physical Review Letters

Mesoscopic Superposition States Generated by Synthetic Spin-Orbit Interaction in Fock-State Lattices

Dawei Wang, Han Cai, Ren‐Bao Liu, Marlan O. Scully

Published Jun 2, 2016• 65 citations
arXivHTMLPDF

Abstract

Mesoscopic superposition states of photons can be prepared in three cavities interacting with the same two-level atom. By periodically modulating the three cavity frequencies around the transition frequency of the atom with a 2π/3 phase difference, the time reversal symmetry is broken and an optical circulator is generated with chiralities depending on the quantum state of the atom. A superposition of the atomic states can guide photons from one cavity to a mesoscopic superposition of the other two cavities. The physics can be understood in a finite spin-orbit-coupled Fock-state lattice where the atom and the cavities carry the spin and the orbit degrees of freedom, respectively. This scheme can be realized in circuit QED architectures and provides a new platform for exploring quantum information and topological physics in novel lattices.

DOI
10.1103/physrevlett.116.220502

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Mesoscopic superposition states of photons can be prepared in three cavities interacting with the same two-level atom. By periodically modulating the three cavity frequencies around the transition frequency of the atom with a 2π/3 phase difference, the time reversal symmetry is broken and an optical circulator is generated with chiralities depending on the quantum state of the atom. A superposition of the atomic states can guide photons from one cavity to a mesoscopic superposition of the other two cavities. The physics can be understood in a finite spin-orbit-coupled Fock-state lattice where the atom and the cavities carry the spin and the orbit degrees of freedom, respectively. This scheme can be realized in circuit QED architectures and provides a new platform for exploring quantum information and topological physics in novel lattices.
We show that Schrodinger cat states of photons can be prepared with effective magnetic fields gated by the quantum states of a two-level atom interacting with three cavities. By periodically modulating the cavity frequencies with different phases, opposite effective magnetic fields in the Fock-state lattice of cavity photons can be created for the two quantum states of the atom. A superposition of atomic states can guide photons from one cavity to a macroscopic superposition of the other two cavities. This mechanism provides a new platform for exploring quantum information and topological physics in novel lattices.
Schr\odinger cat states of photons can be prepared by effective gauge fields gated by the quantum states of a two-level atom interacting with three cavities. By periodically modulating the cavity frequencies with different phases, opposite effective gauge fields of cavity photons can be created for the two quantum states of the atom. A superposition of atomic states can transport photons from one cavity to a macroscopic superposition of the other two cavities. This mechanism provides new possibilities in exploring quantum entanglement and has applications in quantum metrology and quantum information.
In this study, we explore the breaking of time-reversal symmetry in a scalable cavity quantum electrodynamics (QED) lattice. Such a lattice consists of triangular cells of three cavities coupled to a two-level atom. We synthesize artificial magnetic fields to enable the chiral transfer of photons by sinusoidally modulating the cavity frequencies. Considering various configurations with different numbers of cells in the system, we analyze the circulation of photons and investigate the effect of the frequency modulation on the control of the state transfer in the system. We show the breaking and sustaining of time-reversal symmetry in certain system geometries and consider the scalability of the generating synthetic magnetic field in the system. Our study highlights the potential of scalable cavity QED lattices with synthetic magnetic fields as a versatile tool for investigating quantum phenomena and shows the utility of these systems to serve as test beds for the simulation of condensed matter systems in quantum optical settings.
Chiral quantum state circulation is the unidirectional transfer of a quantum state from one subsystem to the next. It is essential to the working of a quantum computer; for instance, for state preparation and isolation. We propose a cavity-QED architecture consisting of three cavities coupled to a qubit, in which \emph{any} photonic state of cavity 1 with sufficiently many photons circulates to cavity 2 after a fixed time interval, and then to cavity 3 and back to 1. Cavity-state circulation arises from topologically protected chiral boundary states in the associated photon lattice and is thus robust to perturbation. We compute the circulation period in the semi-classical limit, demonstrate that circulation persists for time-scales diverging with the total photon number, and provide a Floquet protocol to engineer the desired Hamiltonian. Superconducting qubits offer an ideal platform to build and test these devices in the near term.
In this dissertation we focused on two topics: 1. atomic cooperative effect, including superradiance, subradiance and collective Lamb shift in an atomic ensemble; 2. novel topological effect in quantum optics system, such as Haldane model, synthetic magnetic field in superradiance lattice and synthetic spin-orbit interaction in Fock-state lattices. \n\nIn the first part, we start from the Dicke state, an N-particle atomic ensemble excited by a single photon. Due to the interaction of the atoms with a continuum of vacuum modes, the Dicke state has a larger decay rate compared with an isolated atom, termed the single photon superradiance. In the “opposite” case, the single-photon subradiance state does not decay because of the destructive interference of the atomic transitions. We study the protection of subradiant states by the symmetry of the atomic distributions in the Dicke limit, in which collective Lamb shifts cannot be neglected. We find that antisymmetric states are subradiant states for distributions with reflection symmetry. Continuous symmetry can also be used to achieve subradiance in an extended ensemble. This study is relevant to the problem of robust quantum memory with long storage time and fast readout.\n\nIn the second part, we start from introducing the concepts, methods, and models from quantum optics or condensed matter physics. They include the timed-Dicke states, electromagnetically induced transparency, coupled wave equations, tight-binding model, band theory, Floquet theory, superradiance lattice, integer quantum Hall effect, Haldane model, etc.. Based upon these tools, we study three topological quantum optics systems: (i) a Haldane model with in situ tunable topological properties in a two-dimensional momentumspace superradiance lattice composed of timed Dicke states in electromagnetically induced transparency; (ii) a spin-orbit coupled Fock-state lattice, which introduce a novel quantum operation to generate mesoscopic superposition states, e.g., the NOON states and cat states; (iii) a synthetic magnetic field created in a quasi one dimensional superradiance lattice, which is predicted to be observed in thermal vapours of alkali atoms instead of only in cold atoms (as in previous experiments). This study aims to provide a novel, highly tunable platform simulating exotic phenomena in condensed matter physics and offers a basis of topological quantum optics and novel photonic devices.
We propose a scheme to generate superposition and entanglement between the mesoscopic squeezed vacuum states by considering the two-photon interaction of NNN two-level atoms in a cavity with high quality factor, assisted by a strong driving field. By virtue of specific choices of the cavity detuning, a number of multiparty entangled states can be prepared, including the entanglement between the atomic and the squeezed vacuum cavity states and between the squeezed vacuum states and the coherent states of the cavities. We also present how to prepare entangled states and ``Schr\"odinger cats'' states regarding the squeezed vacuum states of the cavity modes. The possible extension and application of our scheme are discussed. Our scheme is close to the reach with current cavity QED techniques.