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arXiv:1006.0762 · Physical Review A

Time-reversal-symmetry breaking in circuit-QED-based photon lattices

Jens Koch, Andrew Houck, Karyn Le Hur, S. M. Girvin

Published Oct 11, 2010• 394 citations
arXivHTMLPDF

Abstract

Breaking time-reversal symmetry is a prerequisite for accessing certain interesting many-body states such as fractional quantum Hall states. For polaritons, charge neutrality prevents magnetic fields from providing a direct symmetry-breaking mechanism and, similar to the situation in ultracold atomic gases, an effective magnetic field has to be synthesized. We show that in the circuit-QED architecture, this can be achieved by inserting simple superconducting circuits into the resonator junctions. In the presence of such coupling elements, constant parallel magnetic and electric fields suffice to break time-reversal symmetry. We support these theoretical predictions with numerical simulations for realistic sample parameters, specify general conditions under which time reversal is broken, and discuss the application to chiral Fock-state transfer, an on-chip circulator, and tunable band structure for the Kagome lattice.

DOI
10.1103/physreva.82.043811

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Breaking time-reversal symmetry is a prerequisite for accessing certain interesting many-body states such as fractional quantum Hall states. For polaritons, charge neutrality prevents magnetic fields from providing a direct symmetry-breaking mechanism and, similar to the situation in ultracold atomic gases, an effective magnetic field has to be synthesized. We show that in the circuit-QED architecture, this can be achieved by inserting simple superconducting circuits into the resonator junctions. In the presence of such coupling elements, constant parallel magnetic and electric fields suffice to break time-reversal symmetry. We support these theoretical predictions with numerical simulations for realistic sample parameters, specify general conditions under which time reversal is broken, and discuss the application to chiral Fock-state transfer, an on-chip circulator, and tunable band structure for the Kagome lattice.
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.
Quantum many-body systems in which time-reversal symmetry is broken give rise to a wealth of exotic phases, and thus constitute one of the frontiers of modern condensed matter physics. Quantum simulation allows us to better understand many-body systems with huge Hilbert space, where classical simulation is usually inefficient. With superconducting quantum circuit as a platform for quantum simulation, we realize synthetic Abelian gauge fields by using microwave drive and tunable coupling in loop configurations to break the time-reversal symmetry of the system. Based on high-precision manipulation and readout of circuit-QED architecture, we demonstrate the chiral ground spin current of a time-reversal symmetry broken system with nontrivial interactions. Our work is a significant attempt to simulate quantum many-body systems with time-reversal symmetry breaking in multi-qubit superconducting processors.
The recent rapid advancement in the ability to create and manipulate superconducting qubit systems has created an exciting opportunity to construct quantum materials from the ground up, artificial atom by atom. This thesis will explore the creation of a new architecture of quantum simulation in which we use the circuit quantum electrodynamics toolbox to build quantum topological materials that so far have proven difficult to understand with theory, simulate with computational methods, and realize/measure with other quantum systems. Specifically we design a two-dimensional material in which microwave photons living in a superconducting 3D microwave cavity lattice interact strongly with a time-reversal symmetry breaking magnetic field and with each other. This is the first photonic topological lattice platform compatible with strong interactions. The combination of these interactions will enable the study of fractional quantum Hall systems, where fractionally charged particles called anyons are theorized to exist. This thesis describes how to engineer a tunable, low loss microwave lattice, create a magnetic field for chargeless photons using ferrite crystals, and generate inter-particle interactions using Josephson junction transmon qubits.
Synthetic fields applied to ultracold quantum gases can realize topological phases that transcend conventional Bose and Fermi-liquid paradigms. Raman laser beams in particular are under scrutiny as a route to create synthetic fields in neutral gases to mimic ordinary magnetic and electric fields acting on charged matter. Yet external laser beams can impose heating and losses that make cooling into many-body topological phases challenging. We propose that atomic or molecular dipoles placed in optical lattices can realize a topological phase without synthetic fields by placing them in certain frustrated lattices. We use numerical modeling on a specific example to show that the interactions between dipolar fermions placed in a kagome optical lattice spontaneously break time-reversal symmetry to lead to a topological Mott insulator, a chiral topological phase generated entirely by interactions. We estimate realistic entropy and trapping parameters to argue that this intriguing phase of matter can be probed with quantum gases using a combination of recently implemented technologies.
Time-reversal-symmetry breaking (TRSB) has been central to detecting exotic phases of matter. Here, we leverage the circuit electrodynamics capabilities of superconducting devices to propose a scheme based on a multimode superconducting ring resonator for the sensitive probing of TRSB in quantum materials. A ring resonator enables nonlinear cross-interactions between the modes which act as built-in amplifiers to be harnessed for enhanced sensing. Using a driven-dissipative model, we explore the nonlinear dynamics of a two-mode superconducting circuit with self- and cross-Kerr nonlinearities under conditions near the bifurcation threshold. By mapping the optimal parameter regimes, we show that even when the photon occupation numbers are subjected to different initial conditions, they can be driven into a symmetric configuration which is broken even with weak TRSB. Through a full quantum analysis we demonstrate that the Kerr-nonlinear interactions up-convert the magnetic effects of the material-resonator hybrid system, enhancing the probing of TRSB. Our findings highlight the utility of superconducting microwave resonators outside of quantum information processing, as a tool for probing exotic states of matter.
A chiral photonic interface is a quantum system that has different probabilities for emitting photons to the left and right. An on-chip compatible chiral interface is attractive for both fundamental studies of light-matter interactions and applications to quantum information processing. We propose such a chiral interface based on superconducting circuits, which has wide bandwidth, rich tunability, and high tolerance to fabrication variations. The proposed interface consists of a core that uses Cooper-pair boxes (CPBs) to break time-reversal symmetry, and two superconducting transmons that connect the core to a waveguide in the manner reminiscent of a "giant atom." The transmons form a state decoupled from the core, akin to dark states of atomic physics, rendering the whole interface insensitive to the CPB charge noise. The proposed interface can be extended to realize a broadband fully passive on-chip circulator for microwave photons.