Macroscopic Quantum Superposition Research Articles

Rabi oscillations and macroscopic quantum superposition states

A two-level atom interacting with a single radiation mode is considered, without the rotating-wave approximation, in the strong-coupling regime. It is shown that, in agreement with the recent results on Rabi oscillations in a Josephson junction [Y. Nakamura, Yu. A. Pashkin, and J. S. Tsai, Phys. Rev. Lett. 87, 246601 (2001)], the Rabi frequency is indeed proportional to first kind integer order Bessel functions in the limit of a large number of photons and the dressed states are macroscopic quantum superposition states. To approach this problem, analytical use of the dual Dyson series and the rotating-wave approximation is made.

Critical quantum fluctuations in the degenerate parametric oscillator

We develop a systematic theory of critical quantum fluctuations in the driven parametric oscillator. Our analytic results agree well with stochastic numerical simulations. We also compare the results obtained in the positive-P representation, as a fully quantum-mechanical calculation, with the truncated Wigner phase-space equation, also known as the semiclassical theory. We show when these results agree and differ in calculations taken beyond the linearized approximation. We find that the optimal broadband noise reduction occurs just above threshold. In this region where there are large quantum fluctuations in the conjugate variance and macroscopic quantum superposition states might be expected, we find that the quantum predictions correspond very closely to the semiclassical theory.

Macroscopic quantum superposition states in Bose-Einstein condensates: Decoherence and many modes

We investigate the feasibility of a particular scheme for generating macroscopic quantum superposition states in two-species dilute gas Bose-Einstein condensates. The scheme utilizes two-body interactions and Josephson coupling between the species. We report numerical studies that extend a previous two-mode model to include dissipation and extra modes.

Equivalence between macroscopic quantum superpositions and maximally entangled states: Application to phase-shift detection

We demonstrate that the superpositions of macroscopically distinct coherent states are maximally entangled states. Among other possible applications of this result, in this paper we show that the experimental arrangements generating superpositions of macroscopically distinct coherent states may be adapted for precision phase-shift detection reaching the maximum sensitivity allowed by quantum physics (Heisenberg limit).

Macroscopic quantum superposition ofcurrent states in a Josephson-junction loop

Superconducting circuits with Josephson tunneljunctions are interesting systems for research on quantum-mechanical behavior of macroscopic degrees of freedom.A particular realization is a small superconducting loopcontaining three Josephson junctions. Close to magneticfrustration 1/2, the physics of this system corresponds to adouble well, whose minima correspond to persistent currents ofopposite sign. We present DC measurements of the fluxindicating a smooth transition close to the degeneracy pointeven at very low temperatures. Furthermore, microwave-spectroscopy experiments allow for the excitation to the nextexcited state. The dependence of the energy of the resonance onthe applied flux clearly indicates the nature of these states astunneling-splitted superpositions of flux states. We theoretically analyze the system using a generalized master-equationformulation of the spin-boson model. We address the nature ofthe measuring process by a switching DC SQUID and thepossible interpretation of the spectroscopy data in terms ofquantum coherence. We discuss these aspects in the context offurther applications as a quantum bit.

Generation of two-mode nonclassical motional states and a Fredkin gate operation in a two-dimensional ion trap

We present an efficient scheme to generate two-mode SU(2) macroscopic quantum superposition (Schr\"odinger cat) states, entangled number states and entangled coherent states for the vibrational motion of an ion trapped in a two-dimensional harmonic potential well. We also show that the same scheme can be used to realize a Fredkin gate operation.

Macroscopic Quantum Superposition States in a Model of Photon-Supersonic Phonon Interaction

A model of photon-hypersonic phonon interaction is proposed. The evolution of macroscopic quantum superposition states is analyzed, including the wave function and number distribution. It is shown that a superposition state of hypersonic phonon modes can be generated in the case of nondetuning and no losses.

Decoherence in Bose-Einstein condensates: Towards bigger and better Schrödinger cats

We consider a quantum superposition of Bose-Einstein condensates (BEC's) in two immiscible internal states. A decoherence rate for the resulting Schr\"odinger cat is calculated and shown to be a significant threat to this macroscopic quantum superposition of BEC's. An experimental scenario is outlined where the decoherence rate due to the thermal cloud is dramatically reduced thanks to trap engineering and ``symmetrization'' of the environment, which allow the Schr\"odinger cat to be an approximate pointer state.

Decoherence of quantum superpositions through coupling to engineered reservoirs

The theory of quantum mechanics applies to closed systems. In such ideal situations, a single atom can, for example, exist simultaneously in a superposition of two different spatial locations. In contrast, real systems always interact with their environment, with the consequence that macroscopic quantum superpositions (as illustrated by the 'Schrodinger's cat' thought-experiment) are not observed. Moreover, macroscopic superpositions decay so quickly that even the dynamics of decoherence cannot be observed. However, mesoscopic systems offer the possibility of observing the decoherence of such quantum superpositions. Here we present measurements of the decoherence of superposed motional states of a single trapped atom. Decoherence is induced by coupling the atom to engineered reservoirs, in which the coupling and state of the environment are controllable. We perform three experiments, finding that the decoherence rate scales with the square of a quantity describing the amplitude of the superposition state.

Finite Kerr medium: Macroscopic quantum superposition states and Wigner functions on the sphere

We propose a spin model which exhibits the main properties of the Kerr medium. The description of the model uses a recently generalized quasiprobability distribution (Wigner function) for the SU(2) group. This function is naturally defined on the sphere, which plays the role of phase space for the spin system. Our model leads to macroscopic quantum superposition states on the sphere.

Generation of optical macroscopic quantum superposition states via state reduction with a Mach-Zehnder interferometer containing a Kerr medium

A method for producing macroscopic quantum superposition states (generally known as Schr\"odinger cat) states for optical fields is presented. The proposed method involves two modes of the field interacting dispersively in a Kerr medium where one of the modes is an arm of a Mach-Zehnder interferometer and the other mode is external to it. If the external mode initially contains a macroscopic quantum state, such as a coherent state, and the vacuum and a single photon state are the inputs to the interferometer, the external field state becomes entangled with the number states associated with the two paths of the interferometer. Selective measurement at the output ports of the interferometer project the external mode into the desired cat states. It is pointed out that the method can also be used to generate cat states out of multimode states initially containing correlations.

Non-Markovian quantum state diffusion

A nonlinear stochastic Schr\"odinger equation for pure states describing non-Markovian diffusion of quantum trajectories and compatible with non-Markovian master equations is presented. This provides an unraveling of the evolution of any quantum system coupled to a finite or infinite number of harmonic oscillators without any approximation. Its power is illustrated by several examples, including measurementlike situations, dissipation, and quantum Brownian motion. Some examples treat this environment phenomenologically as an infinite reservoir with fluctuations of arbitrary correlation. In other examples the environment consists of a finite number of oscillators. In such a quasiperiodic case we see the reversible decay of a macroscopic quantum-superposition (``Schr\"odinger cat''). Finally, our description of open systems is compatible with different positions of the ``Heisenberg cut'' between system and environment.

PRODUCTION AND DETECTION OF SCHRDINGER CAT STATE AND ITS EFFECT ON THE EVOLUTION OF JAYNES-CUMMINGS MODEL

In this article, we have studied how to generate macroscopic quantum superposition states in electromagnetic field, the Schrodinger cat states, from the large-detuning degenerate Raman process and the large-detuning two-photon Jaynes-Cummings model. The homodyne detection of these states is also discussed. When the initial state of the field is the Schrodinger cat state, the effects of the cat state on the collapse and revival phenomena in the intensity-dependent Jaynes-Cummings model are investigated. The revival in varying degrees occurs in the collapse region resulted from the evolution of initial coherent state.

Creating metastable Schrödinger cat states.

We propose a scheme using feedback to generate a macroscopic quantum superposition of coherent states in an optical cavity mode which experiences very little decoherence (due to dissipation).

Transient macroscopic quantum superposition states in degenerate parametric oscillation: Calculations in the large-quantum-noise limit using the positive P representation.

Recent work by Wolinsky and Carmichael $[---OSA Annual Meeting, 1989 Technical Digest Series Vol. 18 (Optical Society of America, Washington, DC, 1989)] suggests that a superposition of two macroscopically distinct coherent states (a ``Schr\"odinger-cat'' state) may be produced in degenerate parametric oscillation in a transient regime. We investigate this possibility by performing numerical simulations of quantum stochastic equations derived using the positive P representation. The equations allow for finite signal cavity loss. Interference fringes which indicate the existence of the macroscopic superposition states are indeed predicted in regimes where the parametric nonlinearity is sufficiently large compared to the signal cavity losses. Experimental criteria needed for the generation of macroscopic quantum superposition states using parametric oscillation are thus established.

Evolution of Coherent States in a Dispersionless Fibre with Saturable Nonlinearity and the Generation of Macroscopic Quantum-superposition States

Abstract We study the evolution of a initially coherent state of an electromagnetic field propagating in a Kerr medium with saturable nonlinearity. By using the quantum phase distribution formalism, we analyse the dependence of the output signal phase configuration upon input field amplitude. We observe that the saturation of the nonlinear contribution of the refractive index of the propagation medium introduces interference effects that compromise the observation of macroscopically well distinguishable components of the output state. For input amplitudes much larger than a characteristic saturation amplitude the final state differs from the input state only by an overall phase shift. Possible relevance of the present results in the experimental search of Schrodinger cat-like states using semiconductor-doped glass optical fibres is discussed.

Linewidth prevents macroscopic quantum superposition generation by single atom dispersion

A method for generating macroscopically distinguishable superposition states via single atom dispersion was proposed by Savage et al. see Optics Letters, vol.15, p.628, 1990. In that model, the atomic linewidth was not considered. However, including the atomic linewidth, the authors get two contradictory conditions for the generation of distinguishable superposition states. This shows that the atomic linewidth prevents the formation of macroscopically distinguishable superposition states by the proposed method.

Back-action in the measurement of “macroscopic quantum superpositions” in microwave cavities

We analyze the back-action of nonlinear atomic homodyning measurements on steady-state “macroscopic superpositions” that can be generated in high-Q microwave cavities. We show that a full characterization of the state requires measurements such that the macroscopic superposition is irreversibly destroyed, that is, it cannot be reconstructed by using the scheme that was used to generate it in the first place.

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

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.

Nonlinear atomic homodyne detection: A technique to detect macroscopic superpositions in a micromaser.

We propose a measurement scheme to detect the multiphoton coherences inherent in the macroscopic quantum superpositions that can be generated in a superconducting micromaser cavity. The scheme is a nonlinear version of a single-atom homodyne detector. It is shown that the ionization probability of a single test atom is given in terms of the Wigner characteristic function of the field.