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arXiv:1109.1199 · Physical Review A

Two-frequency Jahn-Teller systems in circuit QED

Tekin Dereli, Yusuf Gül, P. Forn-Díaz, Özgür Esat Müstecaplıoğlu

Published May 30, 2012• 15 citations
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Abstract

We investigate the simulation of Jahn-Teller models with two nondegenerate vibrational modes using a circuit QED architecture. Typical Jahn-Teller systems are anisotropic and require at least a two-frequency description. The proposed simulator consists of two superconducting lumped-element resonators interacting with a common flux qubit in the ultrastrong coupling regime. We translate the circuit QED model of the system to a two-frequency Jahn-Teller Hamiltonian and calculate its energy eigenvalues and the emission spectrum of the cavities. It is shown that the system can be systematically tuned to an effective single-mode Hamiltonian from the two-mode model by varying the coupling strength between the resonators. The flexibility in manipulating the parameters of the circuit QED simulator permits the isolation of the effective single-frequency and pure two-frequency effects in the spectral response of Jahn-Teller systems.

DOI
10.1103/physreva.85.053841

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Bulletin of the American Physical Society•Mar 18, 2010•0 citations
We investigate the simulation of Jahn-Teller models with two nondegenerate vibrational modes using a circuit QED architecture. Typical Jahn-Teller systems are anisotropic and require at least a two-frequency description. The proposed simulator consists of two superconducting lumped-element resonators interacting with a common flux qubit in the ultrastrong coupling regime. We translate the circuit QED model of the system to a two-frequency Jahn-Teller Hamiltonian and calculate its energy eigenvalues and the emission spectrum of the cavities. It is shown that the system can be systematically tuned to an effective single-mode Hamiltonian from the two-mode model by varying the coupling strength between the resonators. The flexibility in manipulating the parameters of the circuit QED simulator permits the isolation of the effective single-frequency and pure two-frequency effects in the spectral response of Jahn-Teller systems.
We theoretically study a circuit QED architecture based on a superconducting flux qubit directly coupled to the center conductor of a coplanar waveguide transmission-line resonator. As already shown experimentally [A. A. Abdumalikov, Jr. et al., Phys. Rev. B 78, 180502(R) (2008)], the strong coupling regime of cavity QED can readily be achieved by optimizing the local inductance of the resonator in the vicinity of the qubit. In addition to yielding stronger coupling with respect to other proposals for flux qubit based circuit QED, this approach leads to a qubit-resonator coupling strength ggg which does not scale as the area of the qubit but is proportional to the total inductance shared between the resonator and the qubit. Strong coupling can thus be attained while still minimizing sensitivity to flux noise. Finally, we show that by taking advantage of the large kinetic inductance of a Josephson junction in the center conductor of the resonator can lead to coupling energies of several tens of percent of the resonator frequency, reaching the ultrastrong coupling regime of cavity QED where the rotating-wave approximation breaks down. This should allow an on-chip implementation of the $E\ensuremath{\bigotimes}\ensuremath{\beta}$ Jahn-Teller model.
Abstract We explore quantum correlations, in particular, quantum entanglement, among vibrational phonon modes as well as between electronic and vibrational degrees of freedom in molecular systems, described by Jahn-Teller mechanism. Specifically, to isolate and simplify the phonon- electron interactions in a complex molecular system, the basis of our discussions is taken to be the proposal of simulating two-frequency Jahn- Teller systems using superconducting circuit quantum electrodynamics systems (circuit QED) by Tekin Dereli and co-workers in 2012. We evaluate the quantum correlations, in particular entanglement between the vibrational phonon modes, and present analytical explanations using a single privileged Jahn-Teller mode picture. Furthermore, spin-orbit entanglement or quantum correlations between electronic and vibrational degrees of freedom are examined. We conclude by discussing experimental feasibility to detect such quantum correlations, considering the dephasing and decoherence in state-of-the-art superconducting two-level systems (qubits).
We consider the nonlinear effects in a Jahn–Teller (JT) system of two coupled resonators interacting simultaneously with a flux qubit using coupled SQUIDs. A two-frequency description of JT system that inherits the networked structure of both nonlinear Josephson junctions and harmonic oscillators is employed to describe the synchronous structures in a multifrequency scheme. Eigenvalue spectrum is used to show the switch between the effective single mode and two mode configuration in terms of frequency difference. The Rabi supersplitting is investigated by the spectral response of JT systems in different coupling regimes. Second-order coherence functions are employed to investigate antibunching effects in resonator mode. Synchronous structure between correlations of privileged mode and qubit is obtained in localization–delocalization and photon blockade regime controlled by the population imbalance.
Cavity quantum electrodynamics (QED) investigates the interaction between resonator-confined radiation and natural atoms. Similar phenomena can be explored using superconducting artificial atoms coupled to microwave resonators. Here, we examine incoherent and coherent spectra in a circuit QED system consisting of a flux qubit coupled to an LC resonator, considering different coupling configurations to the output transmission line. Although such systems can be effectively described by the quantum Rabi model, we demonstrate that the choice of the coupling between the resonator and the input-output channel can significantly affect the emission properties, particularly in the ultrastrong coupling regime. Specifically, we show that when the resonator is capacitively coupled with the input-output transmission line, the spectral features at zero flux offset can be mapped onto those of the cavity QED model. However, this correspondence breaks down for the mutual inductive coupling case. Extending our analysis to the parity-symmetry broken regime of the flux qubit, we further highlight how capacitive and inductive coupling mechanisms lead to distinct spectral features, emphasizing the necessity of a careful input-output treatment for an accurate description of the emission processes.
We study a circuit QED setup where multiple superconducting qubits are ultrastrongly coupled to a single radio-frequency resonator. In this extreme parameter regime of cavity QED the dynamics of the electromagnetic mode is very slow compared to all other relevant timescales and can be described as an effective particle moving in an adiabatic energy landscape defined by the qubits. The focus of this paper is placed on settings with two or multiple qubits, where different types of symmetry-breaking transitions in the ground- and excited-state potentials can occur. Specifically, we show how the change in the level structure and the wave-packet dynamics associated with these transition points can be probed via conventional excitation spectra and Ramsey measurements performed at GHz frequencies. More generally, this analysis demonstrates that state-of-the-art circuit QED systems can be used to access a whole range of particlelike quantum-mechanical phenomena beyond the usual paradigm of coupled qubits and oscillators.
We introduce a systematic formalism for two-resonator circuit QED, where two on-chip microwave resonators are simultaneously coupled to one superconducting qubit. Within this framework, we demonstrate that the qubit can function as a quantum switch between the two resonators, which are assumed to be originally independent. In this three-circuit network, the qubit mediates a geometric second-order circuit interaction between the otherwise decoupled resonators. In the dispersive regime, it also gives rise to a dynamic second-order perturbative interaction. The geometric and dynamic coupling strengths can be tuned to be equal, thus permitting to switch on and off the interaction between the two resonators via a qubit population inversion or a shifting of the qubit operation point. We also show that our quantum switch represents a flexible architecture for the manipulation and generation of nonclassical microwave field states as well as the creation of controlled multipartite entanglement in circuit QED. In addition, we clarify the role played by the geometric interaction, which constitutes a fundamental property characteristic of superconducting quantum circuits without a counterpart in quantum-optical systems. We develop a detailed theory of the geometric second-order coupling by means of circuit transformations for superconducting charge and flux qubits. Furthermore, we show the robustness of the quantum switch operation with respect to decoherence mechanisms. Finally, we propose a realistic design for a two-resonator circuit QED setup based on a flux qubit and estimate all the related parameters. In this manner, we show that this setup can be used to implement a superconducting quantum switch with available technology.