Matter wave interference using two-level atoms and resonant optical fields

A theory of matter wave interference is developed in which resonant optical fields interact with two-level atoms. When recoil effects are included, spatial modulation of the atomic density can occur for times that are greater than or comparable with the inverse recoil frequency. In this regime, the atoms exhibit matter-wave interference. Two specific atom field geometries are considered. In the first, atoms characterized by a homogeneous velocity distribution are subjected to a single radiation pulse. The pulse excites the atoms which then decay back to the lower state. The spatial modulation of the total atomic density is calculated as a function of $t$, where $t$ is the time following the pulse. In contrast to the normal Talbot effect, the spatially modulated density is not a periodic function of $t,$ owing to spontaneous emission; however, after a sufficiently long time, the contribution from spontaneous processes no longer plays a role and the Talbot periodicity is restored. In the second atom-field geometry, there are two pulses separated by an interval $T$. The atomic velocity distribution in this case is assumed to be inhomogeneously broadened. In contrast to the normal Talbot-Lau effect, the spatially modulated density is not a periodic function of $T$, owing to spontaneous emission; however, for sufficiently long time, the contribution from spontaneous processes no longer plays a role and the Talbot periodicity is restored. The structure of the spatially modulated density is studied, and is found to mirror the atomic density following the first pulse. The spatially modulated atomic density serves as an indirect probe of the distribution of spontaneously emitted radiation.Comment: 14 pages, 3 figure

Spectrum of light scattering from an extended atomic wave packet

The spectrum of the light scattered from an extended atomic wave packet is calculated. For a wave packet consisting of two spatially separated peaks moving on parallel trajectories, the spectrum contains Ramsey-like fringes that are sensitive to the phase difference between the two components of the wave packet. Using this technique, one can establish the mutual coherence of the two components of the wave packet without recombining them.Comment: 4 page

Atom interferometry in the presence of an external test mass

The influence of an external test mass on the phase of the signal of an atom interferometer is studied theoretically. Using traditional techniques in atom optics based on the density matrix equations in the Wigner representation, we are able to extract the various contributions to the phase of the signal associated with the classical motion of the atoms, the quantum correction to this motion resulting from atomic recoil that is produced when the atoms interact with Raman field pulses, and quantum corrections to the atomic motion that occur in the time between the Raman field pulses. By increasing the effective wave vector associated with the Raman field pulses using modified field parameters, we can increase the sensitivity of the signal to the point where the quantum corrections can be measured. The expressions that are derived can be evaluated numerically to isolate the contribution to the signal from an external test mass. The regions of validity of the exact and approximate expressions are determined.Comment: 23 pages, 3 figures, 2 table

Dynamical Stability and Quantum Chaos of Ions in a Linear Trap

The realization of a paradigm chaotic system, namely the harmonically driven oscillator, in the quantum domain using cold trapped ions driven by lasers is theoretically investigated. The simplest characteristics of regular and chaotic dynamics are calculated. The possibilities of experimental realization are discussed.Comment: 24 pages, 17 figures, submitted to Phys. Rev

Meanfield treatment of Bragg scattering from a Bose-Einstein condensate

A unified semiclassical treatment of Bragg scattering from Bose-Einstein condensates is presented. The formalism is based on the Gross-Pitaevskii equation driven by classical light fields far detuned from atomic resonance. An approximate analytic solution is obtained and provides quantitative understanding of the atomic momentum state oscillations, as well as a simple expression for the momentum linewidth of the scattering process. The validity regime of the analytic solution is derived, and tested by three dimensional cylindrically symmetric numerical simulations.Comment: 21 pages, 10 figures. Minor changes made to documen

Simulations of Quantum Logic Operations in Quantum Computer with Large Number of Qubits

We report the first simulations of the dynamics of quantum logic operations with a large number of qubits (up to 1000). A nuclear spin chain in which selective excitations of spins is provided by the gradient of the external magnetic field is considered. The spins interact with their nearest neighbors. We simulate the quantum control-not (CN) gate implementation for remote qubits which provides the long-distance entanglement. Our approach can be applied to any implementation of quantum logic gates involving a large number of qubits.Comment: 13 pages, 15 figure

Avoiding Quantum Chaos in Quantum Computation

We study a one-dimensional chain of nuclear $1/2-$spins in an external time-dependent magnetic field. This model is considered as a possible candidate for experimental realization of quantum computation. According to the general theory of interacting particles, one of the most dangerous effects is quantum chaos which can destroy the stability of quantum operations. According to the standard viewpoint, the threshold for the onset of quantum chaos due to an interaction between spins (qubits) strongly decreases with an increase of the number of qubits. Contrary to this opinion, we show that the presence of a magnetic field gradient helps to avoid quantum chaos which turns out to disappear with an increase of the number of qubits. We give analytical estimates which explain this effect, together with numerical data supportingComment: RevTex, 5 pages including 3 eps-figure

Solid-State Quantum Computer Based on Scanning Tunneling Microscopy

We propose a solid-state nuclear spin quantum computer based on application of scanning tunneling microscopy (STM) and well-developed silicon technology. It requires the measurement of tunneling current modulation caused by the Larmor precession of a single electron spin. Our envisioned STM quantum computer would operate at the high magnetic field ($\sim 10$T) and at low temperature $\sim 1$K.Comment: 3pages RevTex including 2 figure