Statistics of Velocity from Spectral Data: Modified Velocity Centroids

We address the problem of studying interstellar turbulence using spectral line data. We find a criterion when the velocity centroids may provide trustworthy velocity statistics. To enhance the scope of centroids applications, we construct a measure that we term ``modified velocity centroids'' (MVCs) and derive an analytical solution that relates the 2D spectra of the modified centroids with the underlying 3D velocity spectrum. We test our results using synthetic maps constructed with data obtained through simulations of compressible magnetohydrodynamical (MHD) turbulence. We show that the modified velocity centroids (MVCs) are complementary to the the Velocity Channel Analysis (VCA) technique. Employed together, they make determining of the velocity spectral index more reliable and for wider variety of astrophysical situations.Comment: 4 pages, 1 figure, Accepted for publication in ApJ Letters. minor change

Detailed studies of non-linear magneto-optical resonances at D1 excitation of Rb-85 and Rb-87 for partially resolved hyperfine F-levels

Experimental signals of non-linear magneto-optical resonances at D1 excitation of natural rubidium in a vapor cell have been obtained and described with experimental accuracy by a detailed theoretical model based on the optical Bloch equations. The D1 transition of rubidium is a challenging system to analyze theoretically because it contains transitions that are only partially resolved under Doppler broadening. The theoretical model took into account all nearby transitions, the coherence properties of the exciting laser radiation, and the mixing of magnetic sublevels in an external magnetic field and also included averaging over the Doppler profile. Great care was taken to obtain accurate experimental signals and avoid systematic errors. The experimental signals were reproduced very well at each hyperfine transition and over a wide range of laser power densities, beam diameters, and laser detunings from the exact transition frequency. The bright resonance expected at the F_g=1 --> F_e=2 transition of Rb-87 has been observed. A bright resonance was observed at the F_g=2 --> F_e=3 transition of Rb-85, but displaced from the exact position of the transition due to the influence of the nearby F_g=2 --> F_e=2 transition, which is a dark resonance whose contrast is almost two orders of magnitude larger than the contrast of the bright resonance at the F_g=2 --> F_e=3 transition. Even in this very delicate situation, the theoretical model described in detail the experimental signals at different laser detunings.Comment: 11 pages, 9 figure

Observing the spin of a free electron

Long ago, Bohr, Pauli, and Mott argued that it is not, in principle, possible to measure the spin components of a free electron. One can try to use a Stern-Gerlach type of device, but the finite size of the beam results in an uncertainty of the splitting force that is comparable with the gradient force. The result is that no definite spin measurement can be made. Recently there has been a revival of interest in this problem, and we will present our own analysis and quantum-mechanical wave-packet calculations which suggest that a spin measurement is possible for a careful choice of initial conditions

Determination of the phase of an electromagnetic field via incoherent detection of fluorescence

We show that the phase of a field can be determined by incoherent detection of the population of one state of a two-level system if the Rabi frequency is comparable to the Bohr frequency so that the rotating wave approximation is inappropriate. This implies that a process employing the measurement of population is not a square-law detector in this limit. We discuss how the sensitivity of the degree of excitation to the phase of the field may pose severe constraints on precise rotations of quantum bits involving low-frequency transitions. We present a scheme for observing this effect in an atomic beam, despite the spread in the interaction time.Comment: 4 pages, 2 fig

Double Occupancy Errors in Quantum Computing Operations: Corrections to Adiabaticity

We study the corrections to adiabatic dynamics of two coupled quantum dot spin-qubits, each dot singly occupied with an electron, in the context of a quantum computing operation. Tunneling causes double occupancy at the conclusion of an operation and constitutes a processing error. We model the gate operation with an effective two-level system, where non-adiabatic transitions correspond to double occupancy. The model is integrable and possesses three independent parameters. We confirm the accuracy of Dykhne's formula, a nonperturbative estimate of transitions, and discuss physically intuitive conditions for its validity. Our semiclassical results are in excellent agreement with numerical simulations of the exact time evolution. A similar approach applies to two-level systems in different contexts

Velocity Modification of Power Spectrum from Absorbing Medium

Quantitative description of the statistics of intensity fluctuations within spectral line data cubes introduced in our earlier work is extended to the absorbing media. A possibility of extracting 3D velocity and density statistics from both integrated line intensity as well as from the individual channel maps is analyzed. We find that absorption enables the velocity effects to be seen even if the spectral line is integrated over frequencies. This regime that is frequently employed in observations is characterized by a non-trivial relation between the spectral index of velocities and the spectral index of intensity fluctuations. For instance when density is dominated by fluctuations at large scales, i.e. when correlations scale as r^{-\gamma}, \gamma<0, the intensity fluctuations exhibit a universal spectrum of fluctuations ~K^{-3} over a range of scales. When small scale fluctuations of density contain most of the energy, i.e. when correlations scale as r^{-\gamma}, \gamma>0, the resulting spectrum of the integrated lines depends on the scaling of the underlying density and scales as K^{-3+\gamma}. We show that if we take the spectral line slices that are sufficiently thin we recover our earlier results for thin slice data without absorption. As the result we extend the Velocity Channel Analysis (VCA) technique to optically thick lines enabling studies of turbulence in molecular clouds. In addition, the developed mathematical machinery enables a quantitative approach to solving other problems that involved statistical description of turbulence within emitting and absorbing gas.Comment: 51 page, 3 figures. Accepted to Astrophysical Journa

Molecular Emission Line Formation in Prestellar Cores

We investigate general aspects of molecular line formation under conditions which are typical of prestellar cores. Focusing on simple linear molecules, we study formation of their rotational lines by radiative transfer simulations. We present a thermalization diagram to show the effects of collisions and radiation on the level excitation. We construct a detailed scheme (contribution chart) to illustrate the formation of emission line profiles. This chart can be used as an efficient tool to identify which parts of the cloud contribute to a specific line profile. We show how molecular line characteristics for uniform model clouds depend on hydrogen density, molecular column density, and kinetic temperature. The results are presented in a 2D plane to illustrate cooperative effects of the physical factors. We also use a core model with a non-uniform density distribution and chemical stratification to study the effects of cloud contraction and rotation on spectral line maps. We discuss the main issues that should be taken into account when dealing with interpretation and simulation of observed molecular lines.Comment: Accepted for publication in Ap

Frictional quantum decoherence

The dynamics associated with a measurement-based master equation for quantum Brownian motion are investigated. A scheme for obtaining time evolution from general initial conditions is derived. This is applied to analyze dissipation and decoherence in the evolution of both a Gaussian and a Schr\"{o}dinger cat initial state. Dependence on the diffusive terms present in the master equation is discussed with reference to both the coordinate and momentum representations.Comment: 18 pages, 7 figure

Canonical Quantum Teleportation

Canonically conjugated observables such as position-momentum and phase-number are found to play a 3-fold role in the drama of the quantum teleportation. Firstly, the common eigenstate of two commuting canonical observables like phase-difference and number-sum provides the quantum channel between two systems. Secondly, a similar pair of canonical observables from another two systems is measured in the Bell operator measurements.Comment: revtex,4 pages,e-mail:[email protected] www.itp.ac.cn/~suncp; The Institute of Theoretical Physics, Academia Sinica, Beijing 100080, P.R. Chin