In this paper we provide a microscopic derivation of the master equation for the Jaynes-Cummings model with cavity losses. We single out both the differences with the phenomenological master equation used in the literature and the approximations under which the phenomenological model correctly describes the dynamics of the atom-cavity system. Some examples wherein the phenomenological and the microscopic master equations give rise to different predictions are discussed in detail.

We show how the interference between spatially separated states of the center of mass (COM) of a mesoscopic harmonic oscillator can be evidenced by coupling it to a spin and performing solely spin manipulations and measurements (Ramsey Interferometry). We propose to use an optically levitated diamond bead containing an NV center spin. The nano-scale size of the bead makes the motional decoherence due to levitation negligible. The form of the spin-motion coupling ensures that the scheme works for thermal states so that moderate feedback cooling suffices. No separate control or observation of the COM state is required and thereby one dispenses with cavities, spatially resolved detection and low mass-dispersion ensembles. The controllable relative phase in the Ramsey interferometry stems from a gravitational potential difference so that it uniquely evidences coherence between states which involve the whole nano-crystal being in spatially distinct locations.

We propose an interferometric scheme based on an untrapped nano-object subjected to gravity. The motion of the center of mass (c.m.) of the free object is coupled to its internal spin system magnetically, and a free flight scheme is developed based on coherent spin control. The wave packet of the test object, under a spin-dependent force, may then be delocalized to a macroscopic scale. A gravity induced dynamical phase (accrued solely on the spin state, and measured through a Ramsey scheme) is used to reveal the above spatially delocalized superposition of the spin-nano-object composite system that arises during our scheme. We find a remarkable immunity to the motional noise in the c.m. (initially in a thermal state with moderate cooling), and also a dynamical decoupling nature of the scheme itself. Together they secure a high visibility of the resulting Ramsey fringes. The mass independence of our scheme makes it viable for a nano-object selected from an ensemble with a high mass variability. Given these advantages, a quantum superposition with a 100 nm spatial separation for a massive object of 10^{9}  amu is achievable experimentally, providing a route to test postulated modifications of quantum theory such as continuous spontaneous localization.

Abstract. A microscopic derivation of the master equation for the Jaynes-Cummings model with cavity losses is given, taking into account the terms in the dissipator which vary with frequencies of the order of the vacuum Rabi frequency. Our approach allows to single out physical contexts wherein the usual phenomenological dissipator turns out to be fully justified and constitutes an extension of our previous analysis [Scala M. et al. 2007 Phys. Rev. A 75, 013811], where a microscopic derivation was given in the framework of the Rotating Wave Approximation.

Abstract.We derive the master equation of a system of two coupled qubits by taking into account their interaction with two independent bosonic baths. Important features of the dynamics are brought to light, such as the structure of the stationary state at general temperatures and the behaviour of the entanglement at zero temperature, showing the phenomena of sudden death and sudden birth as well as the presence of stationary entanglement for long times. The model here presented is quite versatile and can be of interest in the study of both Josephson junction architectures and cavity-QED.

The reduced dynamics of two interacting qubits coupled to two independent bosonic baths is investigated. The one-excitation dynamics is derived and compared with that based on the resolution of appropriate non-Markovian master equations. The Nakajima-Zwanzig and the time-convolutionless projection operator techniques are exploited to provide a description of the non-Markovian features of the dynamics of the two-qubits system. The validity of such approximate methods and their range of validity in correspondence to different choices of the parameters describing the system are brought to light.

Our papers [1,2] propose an experiment in which the observation of Ramsey fringes would be evidence for a spatial superposition. We analyzed this as a magnetic effect creating a Stern-Gerlach like spin dependent separation of the centre of mass (COM) states in conjunction with a gravitational effect imparting a relative phase between the states. The comment points out that this could be interpreted in a different way. It contends that the interference manifested in the spin states is not due to the spatial separation as the gravity effects can also be interpreted as a Zeeman effect. To support its contention, the comment splits the Hamitonian into parts H 1 and H 2 where only H 1 couples the COM with the spin states, while H 2 imparts the phase factor. However, the periodic factorizability of the COM and the spin states requires the action of H 1 as well. It is this factorizability which makes the phase detectable by a measurement on the spin alone. For instance, if the COM and spin states are not entangled at T /2, the evolution by H 1 alone for an additional time T /2 will not be able to factorise them. This will lead to the Ramsey interference pattern being supressed. Thus the very visibility of the phase due to H 2 hinges on the interference brought about by H 1 . Both treatments (our's and the comment's) are valid and equivalent as they use the same Hamiltonian. In both cases there is a spatial superposition except for certain periodic moments in time (at integer multiples of the oscillator time period T ). In both cases, the absence of coherence in the COM motion (which could be due to decoherence from air molecules for example) would remove these fringes.In the absence of decoherence, an arbitrary initial coherent state |β of the COM and an initial spin statewhere |β(t, ±1) are COM coherent states with the timevarying separation of ∆z(t) = 8λδz ωz (1 − cos ω z t) with δ z = 2mωz being the ground state position spread of the oscillator. Despite the fact that |β(t, ±1) oscillate about centresωz where there are finite magnetic fields, in our approach, the entire inhomogeneous magnetic field term of the Hamitonian is "used up" to accompish the Stern-Gerlach like separation ∆z(t), and is thereby, not available any more to impart a Zeeman phase between the separated states. The integrated gravitational phase shift T 0 mg cos θ∆z(t)dt gives exactly theLet us now clarify that even if the comment's interpretation that the measured signal results from "the common displacement of the COM position of both ±1 states" is adopted, the visibility of this signal is affected by the coherence between the superposed COM states. Consider a case where only the COM motion is decohered: the off diagonal terms |β(t, +1) β(t, −1)| are damped by a factor of e −γ(t) . Then the evolved state at t = N T isThus we see that the spin density matrix has also decohered (thereby lowering the visibility of φ as a relevant parameter, say θ, is varied) despite the fact that the decoherence was exclusively for the COM state [3,4]. In particular...

A master equation approach to the study of environmental effects in the adiabatic population transfer in three-state systems is presented. A systematic comparison with the non-Hermitian Hamiltonian approach [N. V. Vitanov and S. Stenholm, Phys. Rev. A 56, 1463] shows that in the weak coupling limit the two treatments lead to essentially the same results. Instead, in the strong damping limit the predictions are quite different: in particular the counterintuitive sequences in the STIRAP scheme turn out to be much more efficient than expected before. This point is explained in terms of quantum Zeno dynamics.