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Physical Review A

Coupled-qubit Tavis-Cummings scheme for prolonging quantum coherence

Amrit De

Published Jan 13, 2015• 1 citation
Publisher

Abstract

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 $1/f$ noise from randomly fluctuating two-level systems. Simple circuit level details are given for flux qubits.

DOI
10.1103/physreva.91.012317

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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.
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. A new and exact open quantum systems formalism -- the quasi-Hamiltonians for the Dicke model thus reveals how a Bell state 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.
The Tavis-Cummings model for more than one qubit interacting with a common oscillator mode is extended beyond the rotating wave approximation (RWA). We explore the parameter regime in which the frequencies of the qubits are much smaller than the oscillator frequency and the coupling strength is allowed to be ultrastrong. The application of the adiabatic approximation introduced by Irish et al. [Phys. Rev. B 72, 195410 (2005)] for a single-qubit system is extended to the multiqubit case. For a two-qubit system, we identify three-state manifolds of close-lying dressed energy levels and obtain results for the dynamics of intramanifold transitions that are incompatible with results from the familiar regime of the RWA. We exhibit features of two-qubit dynamics that are different from the single-qubit case, including calculations of qubit-qubit entanglement. Both number state and coherent state preparations are considered, and we derive analytical formulas that simplify the interpretation of numerical calculations. Expressions for individual collapse and revival signals of both population and entanglement are derived.
In the strong coupling regime of cavity QED where the characteristic damping rates are orders of magnitude below the coherent coupling, resolved multi-photon resonances can be observed for strong enough driving strength. In a certain frequency range, the external coherent drive field hits multi-photon resonances which correspond to very high order transitions that cannot be excited at the given power of the driving field. We found that in this range the cavity field evolves into a robust semiclassical solution which is the mixture of the vacuum and an excited quasi-classical state. The system is reminiscent of optical bistability, however, here a single atom produces a telegraph signal for the outgoing intensity by switching between two states with large photon number difference. We calculate this behavior also for the Tavis-Cummings model representing three qubits in an existing circuit QED experimental setting.
The exact dynamics of a model consisting of two identical qubits interacting non-resonantly with the electromagnetic field mode of an ideal resonator via single-photon transitions is found in the presence of direct Ising interaction of qubits. The exact solution is used to calculate the two-qubit negativity of qubits in the case of a coherent initial state of qubits and a thermal state of the resonator field. It is shown that in the case of resonant interaction of qubits with the field, the initial atomic coherence leads to a significant increase in the maximum degree of entanglement. The inclusion of direct Ising interaction of qubits can significantly enhance the entanglement of qubits in both coherent and non-coherent initial states of qubits. In the case of non-resonant interaction of qubits and the resonator field, the detuning leads to a weakening of the effect of atomic coherence on the dynamics of qubit entanglement.
We present the analytical solution of the Tavis-Cummings (TC) model for more than one qubit inhomogeneously coupled to a single mode radiation field beyond the rotating-wave approximation (RWA). The significant advantage of the displaced oscillator basis enables us to apply the same truncation techniques adopted in the single qubit Jaynes-Cummings (JC) model to the multiple qubits system. The derived analytical spectrum match perfectly the exact diagonalization numerical solutions of the inhomogeneous TC model in the parameter regime where the qubits transition frequencies are far off-resonance with the field frequency and the interaction strengths reach the ultra-strong coupling regime. The two-qubit TC model is quasi-exactly solvable because part of the spectra can be determined exactly in the homogeneous coupling case with two identical qubits or with symmetric(asymmetric) detuning. By means of the fidelity of quantum states we identify several nontrivial level crossing points in the same parity subspace, which implies that homogeneous coupled two-qubit TC model with ω1=ω2ω_1=ω_2ω1​=ω2​ or ω1±ω2=2ωcω_1\pmω_2=2ω_cω1​±ω2​=2ωc​ is integrable. We further explore the time evolution of the qubit's population inversion and the entanglement behavior taking two qubits as an example. The analytical methods provide unexpectedly accurate results in describing the dynamics of the qubit in the present experimentally accessible coupling regime, showing that the collapse-revival phenomena emerge, survive, and are finally destroyed when the coupling strength increases beyond the ultra-strong coupling regime. The suggested procedure applies readily to the multiple qubits system such as the GHZ state entanglement evolution and quantum entanglement between a single photon and superconducting qubits of particular experiment interest.
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.