Open Quantum System Stochastic Dynamics and the Rotating Wave Approximation

We study the stochastic dynamics of a two-level quantum system interacting with a stochastic magnetic field, and a single frequency electromagnetic field, with and without making the rotating wave approximation (RWA). The transformation to the rotating frame does not commute with the stochastic Hamiltonian if the stochastic field has nonvanishing components in the transverse direction. Hence, making the RWA modifies the stochastic terms in the Hamiltonian. Modification of the decay terms is also required in a master equation approach (i.e., the Liouville--von Neumann density matrix equation) for describing the dynamics. For isotropic Gaussian white noise, the RWA dynamics remains Markovian, although the Lindblad terms in the master equation for the density matrix become time-dependent when the non-commutation of the RWA transformation and the noise Hamiltonian is properly accounted for. We also treat Ornstein--Uhlenbeck noise, and find, in contra-distinction to the white noise case, a significant difference in the dynamics calculated with the RWA when the non-commutation of the RWA transformation and the noise Hamiltonian is taken into account. These findings are applicable to the modeling of any open quantum system coupled to an electromagentic field.Comment: 11 pages, 22 figures. Accepted for publication in J. Phys.

The Dynamics of an Electric Dipole Moment in a Stochastic Electric Field

The mean-field dynamics of an electric dipole moment in a deterministic and a fluctuating electric field is solved to obtain the average over fluctuations of the dipole moment and the angular mo- mentum as a function of time for a Gaussian white noise stochastic electric field. The components of the average electric dipole moment and the average angular momentum along the deterministic electric field direction do not decay to zero, despite fluctuations in all three components of the elec- tric field. This is in contrast to the decay of the average over fluctuations of a magnetic moment in a stochastic magnetic field with Gaussian white noise in all three components. The components of the average electric dipole moment and the average angular momentum perpendicular to the deterministic electric field direction oscillate with time but decay to zero, and their variance grows with time.Comment: 10 pages, 10 figure

Simple spin-orbit based devices for electron spin polarization

We propose quantum devices having spin-orbit coupling (but no magnetic fields or magnetic materials) that, when attached to leads, yield a high degree of transmitted electron polarization. An example of such a simple device is treated within a tight binding model composed of two 1D chains coupled by several consecutive rungs (i.e., a ladder) and subject to a gate voltage. The ensuing scattering problem (with Rashba spin-orbit coupling) is solved, and a sizable polarization is predicted. When the ladder is twisted into a helix (as in DNA), the curvature energy augments the polarization. For a system with random spin-orbit coupling, the distribution of polarization is broad, hence a high degree of polarization can be obtained in a measurement of a given disorder-realization. When disorder occurs in a double helix structure then, depending on scattering energy, the variance of the polarization distribution can increase even further due to helix curvature.Comment: 9 PRB page

Coherence of an Interacting Bose Gas: from a Single to a Double Well

The low energy properties of a trapped bose gas split by a potential barrier are determined over the whole range of barrier heights. We derive a self-consistent two-mode model which reduces, for large $N$, to a Bogoliubov model for low barriers and to a Josephson model for any (asymmetric) double well potential, with explicitly calculated tunneling and pair interaction parameters. We compare the numerical results to analytical results that precisely specify the role of number squeezing and finite temperatures in the loss of coherence

Correlation and Entanglement of Multipartite States

We derive a classification and a measure of classical- and quantum-correlation of multipartite qubit, qutrit, and in general, $n$-level systems, in terms of SU$(n)$ representations of density matrices. We compare the measure for the case of bipartite correlation with concurrence and the entropy of entanglement. The characterization of correlation is in terms of the number of nonzero singular values of the correlation matrix, but that of mixed state entanglement requires additional invariant parameters in the density matrix. For the bipartite qubit case, the condition for mixed state entanglement is written explicitly in terms of the invariant paramters in the density matrix. For identical particle systems we analyze the effects of exchange symmetry on classical and quantum correlation.Comment: 5 pages, 4 figure

Decoherence of Nitrogen Vacancy Centers in Diamond

We model the decoherence and dephasing of nitrogen vacancy (NV) centers in diamond due to a noisy paramagnetic bath, with and without the presence of a rf field that couples levels of the ground electronic state manifold, using a simple quantum mechanical model that allows for analytical solutions. The model treats the NV three-level ground state system in the presence of fluctuating magnetic fields that arise from the environment, and that result in decoherence, dephasing and dissipation. We show that all 9 eigenmodes of the three-level system are coupled to each other due to interaction with the environment, and we discuss consequences for fitting experiments in which decoherence plays a role.Comment: 13 pages, and 13 figure

Bose-Einstein Condensates in Time-Dependent Light Potentials: Adiabatic and Nonadiabatic Behavior of Nonlinear Wave Equations

The criteria for validity of adiabaticity for nonlinear wave equations are considered within the context of atomic matter-waves tunneling from macroscopically populated optical standing-wave traps loaded from a Bose-Einstein condensate. We show that even when the optical standing wave is slowly turned on and the condensate behaves adiabatically during this turn-on, once the tunneling-time between wells in the optical lattice becomes longer than the nonlinear time-scale, adiabaticity breaks down and a significant spatially varying phase develops across the condensate wave function from well to well. This phase drastically affects the contrast of the fringe pattern in Josephson-effect interference experiments, and the condensate coherence properties in general.Comment: 5 pages, 3 figure

Dynamics of a Magnetic Needle Magnetometer: Sensitivity to Landau-Lifshitz-Gilbert Damping

An analysis of a single-domain magnetic needle in the presence of an external magnetic field ${\bf B}$ is carried out with the aim of achieving a high precision magnetometer. We determine the uncertainty $\Delta B$ of such a device due to Gilbert dissipation and the associated internal magnetic field fluctuations that gives rise to diffusion of the magnetic needle axis direction ${\bf n}$ and the needle orbital angular momentum. The levitation of the magnetic needle in a magnetic trap and its stability are also analyzed

Feshbach Resonance in a Tight-Binding Model

The physics of Feshbach resonance is analyzed using an analytic expression for the $s$-wave scattering phase-shift and the scattering length $a$ which we derive within a two-channel tight-binding model. Employing a unified treatment of bound states and resonances in terms of the Jost function, it is shown that for strong inter-channel coupling, Feshbach resonance can occur even when the closed channel does not have a bound state. This may extend the range of ultra-cold atomic systems that can be manipulated by Feshbach resonance. The dependence of the sign of $a$ on the coupling strength in the unitary limit is elucidated. As a by-product, analytic expressions are derived for the background scattering length, the external magnetic field at which resonance occurs, and the energy shift $\varepsilon-\varepsilon_B$, where $\varepsilon$ is the scattering energy and $\varepsilon_B$ is the bound state energy in the closed channel (when there is one).Comment: 5 pages with 1 figures + 6 supplementary material pages with 4 figures. Substantial changes compared with previous versio

Sound waves and modulational instabilities on continuous wave solutions in spinor Bose-Einstein condensates

We analyze sound waves (phonons, Bogoliubov excitations) propagating on continuous wave (cw) solutions of repulsive $F=1$ spinor Bose-Einstein condensates (BECs), such as $^{23}$Na (which is antiferromagnetic or polar) and $^{87}$Rb (which is ferromagnetic). Zeeman splitting by a uniform magnetic field is included. All cw solutions to ferromagnetic BECs with vanishing $M_F=0$ particle density and non-zero components in both $M_F=\pm 1$ fields are subject to modulational instability (MI). MI increases with increasing particle density. MI also increases with differences in the components' wavenumbers; this effect is larger at lower densities but becomes insignificant at higher particle densities. CW solutions to antiferromagnetic (polar) BECS with vanishing $M_F=0$ particle density and non-zero components in both $M_F=\pm 1$ fields do not suffer MI if the wavenumbers of the components are the same. If there is a wavenumber difference, MI initially increases with increasing particle density, then peaks before dropping to zero beyond a given particle density. The cw solutions with particles in both $M_F=\pm 1$ components and nonvanishing $M_F=0$ components do not have MI if the wavenumbers of the components are the same, but do exhibit MI when the wavenumbers are different. Direct numerical simulations of a cw with weak white noise confirm that weak noise grows fastest at wavenumbers with the largest MI, and shows some of the results beyond small amplitude perturbations. Phonon dispersion curves are computed numerically; we find analytic solutions for the phonon dispersion in a variety of limiting cases.Comment: 22 pages, 20 figure