Preparation and detection of macroscopic quantum superpositions by two-photon field-atom interactions

Abstract

We put forward a simple, feasible scheme for the preparation and subsequent detection of macroscopic quantum superposition (MQS) states. It is based on the two-photon model which obtains when a cascade of two atomic transitions is resonant with twice the field frequency. The initial conditions amount to a field in a mixed state characteristic of lasers or masers and an excited atom. The MQS is generated by a conditional measurement of the atomic excitation after an interaction time that determines the relative phase of the MQS components. Remarkably, the MQS is subsequently detected and its phase is inferred by measuring the excitation probability of a second, "probe, " atom, as a function of its interaction time. The realization of the scheme in the optical domain, using dielectric microspheres, is discussed. PACS number(s): 42.50.p, 32.80.t, 42.52.+x Superposed macroscopically distinguishable quantum states of the electromagnetic field, hereafter referred to as macroscopic quantum superpositions (MQS), have aroused considerable interest in recent years [1-9]. Their main appeal is that they constitute potentially realizable "Schrodinger cats" that embody the well-known paradoxical aspect of quantum mechanics [4]. Attention has been focused on a single-mode field in a MQS of two coherent quasiclassical states, with identical mean amplitudes and a fixed relative phase [1,3]. Various rather intricate mechanisms have been proposed for the preparation of such MQS, but none of them has been realized thus far. These mechanisms include the following: (a) Nonlinear evolution of the field from an initially coherent state in amplitude-dispersive [5,6], and, particularly, bistably dispersive [7] media. The generation of MQS states in such media is contingent on dissipative losses being negligible. (b) Quantum measurements (photon counting [8] or quadrature detection [9]) of the field, following its preparation in a nonclassical state, e.g. , in a parametric amplifier. Such schemes are hampered not only by dissipation, but also by the performance of photon detectors that falls short of ideal (unit) efficiency.(c) Interactions of a two-level atom with a quantized single-mode field, describable by the Jaynes-Cummings model (JCM). This model is of fundamental importance in quantum optics [10,11] and is realizable to a very good approximation in high-quality resonators [12]. Certain JCM schemes for the generation of MQS rely on the initial preparation of the atom in a polarized state, i.e. , a coherent superposition of the ground and excited states [13,14]. A more recent scheme [15]exploits a remarkable inherent property of the resonant JCM [16],whereby initial preparation of the atom in the ground or excited state and of the field in a quasiclassical coherent state results in the spontaneous disentanglernent of the atomic and field states, with the field forming a MQS of two quasiclassical states. The limitations of this scheme stem from the complexity of the field evolution in the JCM: (i) It is difficult to exactly character...

The Jaynes-Cummings Model

“…These numbers are substantially larger than in previous optical cat proposals . Sherman and Kurizki (1992) have shown how conditional measurements can be used to generate Schrodinger cats in the JCM .…”

State Evolution in the Two-photon Jaynes-Cummings Model with Initial Squeezed Vacuum and Chaotic Fields

“…The two-photon effective interaction Hamiltonian adopts the simple form [9][10][11][12][13][14][15][16][17][18][19] H= hg(a 2 I e)(gl + a t2 IgXel),…”

“…The revivals of the Rabi oscillations in this model are 0950-0340/95 $1000 © 1995 Taylor & Francis Ltd. both compact and regular, in contrast with the one-photon case [10][11][12][13][14] . Sherman and Kurizki [15] and Garraway et al [16] have proposed a scheme for preparation and subsequent detection of macroscopic quantum superposition states (Schrodinger cats) and Fock states with predictable parameters based on the two-photon JCM . Phoenix and Knight [17] have calculated the entropy in this model and pointed out the periodic recovering of the initial atom-field state occurring under a proper choice of the detuning parameter .…”

Global stability criterion for a quantum feedback control process on a single qubit and exponential stability in case of perfect detection efficiency

“…Physik, Ruhr-Universität, D-44780 Bochum stroys, the measured quantum system itself [2,3]. Theoretical as well as experimental investigation have been intensively made dealing with processes where quantum measurements are utilized constructively, for instance theoretical considerations of measurement determination by the quantum register [4], quantum feedback control by continuous measurements [5,6,7,8], especially in quantum optics [1,9,10,11], stabilization and purification of two-level systems [12,13], conditional measurements of coupled quantum dots by a point contact detector [14,15] or by a SET [16,17,18], and the conditional measurement approach due to Sherman and Kurizki [19] to prepare predetermined field states of atoms trapped in optical QED cavities [20,21,22], as well as a similar approach analyzed for spin squeezing in Cs clocks [23].…”