Persistent photon echoes (revivals) are seen for a large number (N) of two-level molecules (TLMs) prepared initially in the all-down state interacting in a lossless cavity with a photon distribution with a small mean photon number. This case has not been addressed previously revealing characteristic times proportional to the square root of N. Unexpectedly, this behavior is independent of the initial photon distribution (including thermal) and long after the initial echoes die out, they re-emerge completely. Entropy, disentanglement and the Q function are considered with complete disentanglement only occurring at the revival times. Comparison is made to established results.
Persistent photon echoes (revivals) are seen for a large number (N) of two-level molecules (TLMs) prepared initially in the all-down state interacting in a lossless cavity with a photon distribution with a small mean photon number. This case has not been addressed previously revealing characteristic times proportional to the square root of N. Unexpectedly, this behavior is independent of the initial photon distribution (including thermal) and long after the initial echoes die out, they re-emerge completely. Entropy, disentanglement and the Q function are considered with complete disentanglement only occurring at the revival times. Comparison is made to established results.
An ensemble of N two-level molecules prepared in its ground state and sharing a lossless cavity with a weak field does not simply absorb: the intensity collapses and then recurs, in a train of collective photon echoes. Working from the exact solution of the Tavis-Cummings model in the few-photon regime nˉ<N, we confirm the echo time τE=4πN+Δ/g numerically at resonance from N=5 to 400, the small-N end discriminating this form from the alternative 4πN−nˉ+Δ/g in its favor. The initial state requires no preparation, being the ground state. The echo time is independent of the initial photon distribution: coherent, thermal, squeezed and oscillatory-squeezed distributions spanning variances from 2 to 34 all recur together, as does a controlled pair with identical mean and variance differing only in the shape of ρnn. The echo amplitude is not: it varies at the tens-of-percent level at fixed mean, including a factor of 1.8 with the squeezing phase at fixed squeezing strength. Detuning organizes the dynamics into two clean regimes separated by a fragmented crossover, the dispersive-branch echo time approaching one-half the resonant one, and sufficient detuning removes the dependence on the initial Dicke state. For arbitrary initial Dicke state, emission replaces absorption at m≃−N/2+nˉ, and the echo envelope acquires one component per step up the ladder: a single-component echo occurs only at the ground state. A feasibility analysis against a five-qubit superconducting device, with Lindblad simulations of cavity decay and dephasing and full-Hilbert-space disorder simulations, shows the first echoes observable at N∼5-20 on existing hardware: the echo survives the dominant loss channel with contrast ∼e−κτE/2, photons being shielded from cavity decay while resident in the emitters.
In a recent paper Yu and Eberly [Phys. Rev. Lett. 93, 140404 (2004)] have shown that two initially entangled and afterward not interacting qubits can become completely disentangled in a finite time. We study transient entanglement between two qubits coupled collectively to a multimode vacuum field, assuming that the two-qubit system is initially prepared in an entangled state produced by the two-photon coherences, and find the unusual feature that the irreversible spontaneous decay can lead to a revival of the entanglement that has already been destroyed. The results show that this feature is independent of the coherent dipole-dipole interaction between the atoms but it depends critically on whether or not collective damping is present.
From the viewpoints of photon-phase and information-entropy dynamics, we investigate the dynamical behavior of initially one-mode amplitude- and phase-squeezed photon fields interacting with a two-state molecular system. A peculiar behavior of these systems is known to be the collapses and revivals of Rabi oscillation of the molecular population. As shown in previous studies, significant differences are observed in the amplitude and the period of the collapse−revival behavior for these fields. These differences are found to be well-described by the dynamical behavior of the photon phase (the Pegg−Barnett phase and the quasiprobability ( Q function) distributions). The features of these photon-phase dynamics are also found to provide significant influence on the time evolution of the information entropy of the molecule, which characterizes the degree of the entanglement between the molecule and the field.
Abstract. We examine the dynamics of subsystems of bipartite and tripartite quantum systems with nonlinear Hamiltonians. We consider two models which capture the generic features of open quantum systems: a three-level atom interacting with a single-mode radiation field, and a three-level atom interacting with two field modes which do not directly interact with each other. The entanglement of specific initially unentangled states of the atom-field system is examined through the time-varying subsystem von Neumann entropy (SVNE). The counterparts of near-revivals and fractional revivals of the initial state are clearly identifiable in the SVNE in all cases where revival phenomena occur. The MandelQ parameter corresponding to the photon number of a radiation field is obtained as a function of time in both models. In those cases where revivals are absent, a time series analysis of the mean photon number reveals a variety of ergodicity properties (as manifested in return maps, recurrence-time distributions and Lyapunov exponents), depending on the strength of the nonlinearity and the degree of coherence of the initial state of the radiation field(s).
An exact solution of the problem of two two-level atoms with degenerate Raman two-photon transitions interacting with one-mode coherent or thermal radiation field in cavity is presented. Asymptotic solution for system state vector is obtained in the approximation of large initial coherent fields. The atom-field is investigated on the basis of the reduced atomic entropy dynamics. The possibility of the system being initially in a pure disentangled state to revive into this state during the evolution process is shown. Conditions and times of disentanglement are derived. The atom-atom entanglement is investigated with using negativity. The possibility of sudden death and birth of atom-atom entanglement is predicted for a coherent field with large mean photon numbers.
We examine the dynamics of subsystems of bipartite and tripartite quantum systems with nonlinear Hamiltonians. We consider two models which capture the generic features of open quantum systems: a three-level atom interacting with a single-mode radiation field, and a three-level atom interacting with two field modes which do not directly interact with each other. The entanglement of specific initially unentangled states of the atom-field system is examined through the time-varying subsystem von Neumann entropy (SVNE). The counterparts of near-revivals and fractional revivals of the initial state are clearly identifiable in the SVNE in all cases where revival phenomena occur. The Mandel Q parameter corresponding to the photon number of a radiation field is obtained as a function of time in both models. In those cases where revivals are absent, a time series analysis of the mean photon number reveals a variety of ergodicity properties (as manifested in return maps, recurrence-time distributions and Lyapunov exponents), depending on the strength of the nonlinearity and the degree of coherence of the initial state of the radiation field(s).