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arXiv:1211.4187 · Physical Review A

Magnetization-noise-induced collapse and revival of Rabi oscillations in circuit QED

Amrit De, Robert Joynt

Published Apr 29, 2013• 8 citations
arXivHTMLPDF

Abstract

We use a quasi-Hamiltonian formalism to describe the dissipative dynamics of a circuit-QED qubit that is affected by several fluctuating two-level systems with a $1/f$-noise power spectrum. The qubit-resonator interactions are described by the Jaynes-Cummings model. We argue that the presence of pure dephasing noise in such a qubit-resonator system will also induce an energy relaxation mechanism via a fluctuating dipole-coupling term. This random modulation of the coupling is seen to lead to rich physical behavior. For non-Markovian noise, the coupling can either worsen or alleviate decoherence, depending on the initial conditions. The magnetization noise leads to behavior resembling the collapse and revival of Rabi oscillations if the photons are in a coherent state. For a broad distribution of noise couplings, the frequency of these oscillations depends on the mean noise strength. We describe this behavior semianalytically and find it to be independent of the number of fluctuators. This phenomenon could be used as an in situ probe of the noise characteristics.

DOI
10.1103/physreva.87.042336

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We use a quasi-Hamiltonian formalism to describe the dissipative dynamics of a circuit-QED qubit that is affected by several fluctuating two-level systems with a 1/f1/f1/f-noise power spectrum. The qubit-resonator interactions are described by the Jaynes-Cummings model. We argue that the presence of pure dephasing noise in such a qubit-resonator system will also induce an energy relaxation mechanism via a fluctuating dipole-coupling term. This random modulation of the coupling is seen to lead to rich physical behavior. For non-Markovian noise, the coupling can either worsen or alleviate decoherence, depending on the initial conditions. The magnetization noise leads to behavior resembling the collapse and revival of Rabi oscillations if the photons are in a coherent state. For a broad distribution of noise couplings, the frequency of these oscillations depends on the mean noise strength. We describe this behavior semianalytically and find it to be independent of the number of fluctuators. This phenomenon could be used as an in situ probe of the noise characteristics.
We analytically investigate the fidelity dynamics of a Jaynes--Cummings qubit coupled to a single-mode cavity in the presence of stochastic fluctuations of the qubit--cavity coupling. Such fluctuations naturally arise in cavity- and circuit-QED platforms due to fabrication imperfections, control-field noise, mechanical vibrations, and environmental disturbances. Since the qubit--cavity coupling governs the rate of coherent energy and information exchange, understanding the effects of its fluctuations is essential for assessing the performance of quantum communication, quantum sensing, and quantum information-processing protocols. We consider both Gaussian white noise and Ornstein--Uhlenbeck noise with finite correlation time as models for the coupling fluctuations. Exploiting the closed dynamics within each excitation manifold, we derive exact analytical expressions for the noise-averaged density matrix and the fidelity relative to the ideal noiseless evolution. We show that the fidelity is determined by a single decoherence factor governed by the integrated noise correlation function, establishing a direct connection between microscopic coupling fluctuations and macroscopic coherence loss. In the white-noise limit, the fidelity decays exponentially, whereas finite noise correlation times produce nonexponential decay and slower coherence loss. We further show that the crossover between Markovian-like and non-Markovian regimes is controlled by the ratio of the noise correlation rate to the coherent coupling strength, and that decoherence increases with photon number because of the enhanced effective qubit--cavity coupling. These results provide a unified analytical framework for quantifying decoherence induced by stochastic coupling fluctuations and for evaluating the robustness of cavity-QED protocols under correlated noise.
We study the dynamics of the Jaynes-Cummings Model for two level systems (or qubits) interacting with a quantized single mode electromagnetic cavity (or `quantum bus'). We show that there is a time in between the collapse and revival of Rabi oscillations when the state of the qubit sub-system, $| ψ\_{attractor} $, is largely independent of its initial state. This generalizes to many qubits the discovery by Gea-Banacloche for the one qubit case. The qubits in such `attractor' states are not entangled either with the field or among themselves, even if they were in the initial state. Subsequently the entanglement between the qubits revives. Finally, it is argued that the collapse and revival of entanglement and the persistence of `non-classicality' is a generic feature of multiple qubits interacting via a `quantum bus'.
We extend the study of the Jayne–Cummings (JC) model involving a pair of identical two-level atoms (or qubits) interacting with a single mode quantized field. We investigate the effects of replacing the radiation field mode with a composite spin, comprising [Formula: see text] qubits, or spin-1/2 particles. This model is relevant for physical implementations in superconducting circuit QED, ion trap and molecular systems. For the case of the composite spin prepared in a spin coherent state, we demonstrate the similarities of this set-up to the qubits-field model in terms of the time evolution, attractor states and in particular the collapse and revival of the entanglement between the two qubits. We extend our analysis by taking into account an effect due to qubit imperfections. We consider a difference (or “mismatch”) in the dipole interaction strengths of the two qubits, for both the field mode and composite spin cases. To address decoherence due to this mismatch, we then average over this coupling strength difference with distributions of varying width. We demonstrate in both the field mode and the composite spin scenarios that increasing the width of the “error” distribution increases suppression of the coherent dynamics of the coupled system, including the collapse and revival of the entanglement between the qubits.
We investigate qubit entanglement dynamics in a two-qubit cavity system with stochastically fluctuating coupling strength, comparing white noise (Markovian) and Ornstein-Uhlenbeck noise (non-Markovian) processes. We analytically solve the system dynamics for both Fock and coherent cavity states and systematically characterize how initial qubit configurations affect entanglement generation and preservation. Our results reveal distinct dynamical regimes: in the Fock-state cavity, initial states in the single-excitation subspace generate robust qubit entanglement in decoherence-free subspaces, while initially entangled states in the double-excitation subspace exhibit inevitable decay without protective symmetries. For coherent cavities, we identify a critical photon-number threshold in the intermediate coherent-state amplitude regime where dynamics transition from low-frequency to high-frequency entanglement oscillations, while universal entanglement loss occurs at large amplitudes. Remarkable resilience against entanglement sudden death emerges under strong non-Markovian noise with long correlation times, where repeated revivals occur. These findings establish cavity photon statistics and environmental memory time as key control parameters for engineering qubit entanglement dynamics in qubit-cavity systems, revealing how system-environment correlations govern quantum information preservation.
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.
Qubit-qubit interactions can significantly boost quantum coherence times for Bell states. The coherence-time enhancements are, however, not monotonic and there exists a phase where further increasing the interaction is unhelpful. A resonator in a suggested circuit QED-type implementation of the Tavis-Cummings (Dicke) model, is shown to shift this transition point depending on the number of loaded photons. This allows the resonator to amplify the coherence enhancements in certain regimes. The interactions also induce unusual collapse and revival-type behavior for the entanglement dynamics. An exact open quantum system's formalism--(quasi-Hamiltonians for the Dicke model) shows how a Bell state singlet-triplet qubit in a resonator can be protected against 1/f1/f1/f noise from randomly fluctuating two-level systems. Simple circuit level details are given for flux qubits.