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Ancillary qubit spectroscopy of cavity (circuit) QED vacua

Jared Lolli, Alexandre Baksic, Dávid Nagy, Vladimir Manucharyan, Cristiano Ciuti

Published Nov 19, 2014• 1 citation
OpenAlex

Abstract

We investigate theoretically how the spectroscopy of an ancillary qubit can probe cavity (circuit) QED ground states containing photons. We consider three classes of systems (Dicke, Tavis-Cummings and Hopfield-like models), where non-trivial vacua are the result of ultrastrong coupling between N two-level systems and a single-mode bosonic field. An ancillary qubit detuned with respect to the boson frequency is shown to reveal distinct spectral signatures depending on the type of vacua. In particular, the Lamb shift of the ancilla is sensitive to both ground state photon population and correlations. Back-action of the ancilla on the cavity ground state is investigated, taking into account the dissipation via a consistent master equation for the ultrastrong coupling regime. The conditions for high-fidelity measurements are determined.

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We investigate theoretically how the spectroscopy of an ancillary qubit can probe cavity (circuit) QED ground states containing photons. We consider three classes of systems (Dicke, Tavis-Cummings and Hopfield-like models), where non-trivial vacua are the result of ultrastrong coupling between N two-level systems and a single-mode bosonic field. An ancillary qubit detuned with respect to the boson frequency is shown to reveal distinct spectral signatures depending on the type of vacua. In particular, the Lamb shift of the ancilla is sensitive to both ground state photon population and correlations. Back-action of the ancilla on the cavity ground state is investigated, taking into account the dissipation via a consistent master equation for the ultrastrong coupling regime. The conditions for high-fidelity measurements are determined.
We investigate theoretically how the spectroscopy of an ancillary qubit can probe cavity (circuit) QED ground states containing photons. We consider three classes of systems (Dicke, Tavis-Cummings, and Hopfield-like models), where nontrivial vacua are the result of ultrastrong coupling between N two-level systems and a single-mode bosonic field. An ancillary qubit detuned with respect to the boson frequency is shown to reveal distinct spectral signatures depending on the type of vacua. In particular, the Lamb shift of the ancilla is sensitive to both ground state photon population and correlations. Backaction of the ancilla on the cavity ground state is investigated, taking into account the dissipation via a consistent master equation for the ultrastrong coupling regime. The conditions for high-fidelity measurements are determined.
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.
Cavity and circuit QED study light-matter interaction at its most fundamental level. Yet, this interaction is most often neglected when considering the coupling of this system with an environment. In this paper, we show how this simplification, which leads to the standard quantum optics master equation, is at the root of unphysical effects. Including qubit relaxation and dephasing, and cavity relaxation, we derive a master equation that takes into account the qubit-resonator coupling. Special attention is given to the ultrastrong coupling regime, where the failure of the quantum optical master equation is manifest. In this situation, our model predicts an asymmetry in the vacuum Rabi splitting that could be used to probe dephasing noise at unexplored frequencies. We also show how fluctuations in the qubit frequency can cause sideband transitions, squeezing, and Casimir-like photon generation.
The field of cavity quantum electrodynamics (cavity QED) studies the interaction between light and matter on a fundamental level: a single atom interacts with a single photon. If the atom-photon coupling is larger than any dissipative effects, the system enters the strong-coupling limit. A peculiarity of this regime is the possibility to form coherent superpositions of light and matter excitations - a kind of 'molecule' consisting of an atomic and a photonic contribution. The novel research field of circuit QED extends cavity QED concepts to solid-state based system. Here, a superconducting quantum bit is coupled to an on-chip superconducting one-dimensional waveguide resonator. Owing to the small mode-volume of the resonant cavity, the large dipole moment of the 'artificial atom' and the enormous engineering potential inherent to superconducting quantum circuits, remarkable atom-photon coupling strengths can be realized. This thesis describes the theoretical framework, the development of fabrication techniques and the implementation of experimental characterization techniques for superconducting quantum circuits for circuit QED applications. In particular, we study the interaction between superconducting flux quantum bits and high-quality coplanar waveguide resonators in the strong-coupling limit. Furthermore, we report on the first experimental realization of a circuit QED system operating in the ultrastrong-coupling regime, where the atom-photon coupling rate reaches a considerable fraction of the relevant system frequencies. In these experiments we could observe phenomena that can not be explained within the renowned Jaynes-Cummings model.
We study effective light-matter interactions in a circuit QED system consisting of a single LCLCLC resonator, which is coupled symmetrically to multiple superconducting qubits. Starting from a minimal circuit model, we demonstrate that, in addition to the usual collective qubit-photon coupling, the resulting Hamiltonian contains direct qubit-qubit interactions, which have a drastic effect on the ground- and excited-state properties of such circuits in the ultrastrong-coupling regime. In contrast to the superradiant phase transition expected from the standard Dicke model, we find an opposite mechanism, which at very strong interactions completely decouples the photon mode and projects the qubits into a highly entangled ground state. These findings resolve previous controversies over the existence of superradiant phases in circuit QED, but they more generally show that the physics of two- or multiatom cavity QED settings can differ significantly from what is commonly assumed.
We examine a two-level system coupled to a quantum oscillator, typically representing experiments in cavity and circuit quantum electrodynamics. We show how such a system can be treated analytically in the ultrastrong coupling limit, where the ratio $g/\ensuremath{\Omega}$ between coupling strength and oscillator frequency approaches unity and goes beyond. In this regime the Jaynes-Cummings model is known to fail because counter-rotating terms have to be taken into account. By using Van Vleck perturbation theory to higher orders in the qubit tunneling matrix element $\ensuremath{\Delta}$ we are able to enlarge the regime of applicability of existing analytical treatments, including, in particular, also the finite-bias case. We present a detailed discussion on the energy spectrum of the system and on the dynamics of the qubit for an oscillator at low temperature. We consider the coupling strength ggg to all orders, and the validity of our approach is even enhanced in the ultrastrong coupling regime. Looking at the Fourier spectrum of the population difference, we find that many frequencies contribute to the dynamics. They are gathered into groups whose spacing depends on the qubit-oscillator detuning. Furthermore, the dynamics is not governed anymore by a vacuum Rabi splitting which scales linearly with ggg, but by a nontrivial dressing of the tunneling matrix element, which can be used to suppress specific frequencies through a variation of the coupling.