Tuning the adiabaticity of spin dynamics in diamond nitrogen vacancy centers.

We study the spin dynamics of diamond nitrogen vacancy (NV) centers in an oscillating magnetic field along the symmetry axis of the NV in the presence of transverse magnetic fields. It is well-known that the coupling between the otherwise degenerate Zeeman levels |MS= ±1⟩ due to strain and electric fields is responsible for a Landau-Zener process near the pseudo-crossing of the adiabatic energy levels when the axial component of the oscillating magnetic field changes sign. We derive an effective two-level Hamiltonian for the NV system that includes coupling between the two levels via virtual transitions into the third far-detuned level |MS= 0⟩ induced by transverse magnetic fields. This coupling adds to the coupling due to strain and electric fields, with a phase that depends on the direction of the transverse field in the plane perpendicular to the NV axis. Hence, thetotal couplingof the Zeeman levels can be tuned to control the adiabaticity of spin dynamics by fully or partially compensating the effect of the strain and electric fields, or by enhancing it. Moreover, by varying the strength and direction of the transverse magnetic fields, one can determine the strength and direction of the local strain and electric fields at the position of the NV center, and even theexternalstress and electric field. The nuclear spin hyperfine interaction is shown to introduce a nuclear spin dependent offset of the axial magnetic field for which the pseudo-crossing occurs, while the adiabaticity remains unaffected by the nuclear spin. If the NV center is coupled to the environment, modeled by a bath with a Gaussian white noise spectrum, as appropriate for NVs near the diamond surface, then the spin dynamics is accompanied by relaxation of the Zeeman level populations and decoherence with a non-monotonic decrease of the purity of the system. The results presented here have important impact for metrology with NV centers, quantum control of spin systems in solids and coupled dynamics of spin and rotations in levitated nano-objects in the presence of magnetic fields.

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

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

Erratum: Dynamics of an electric dipole moment in a stochastic electric field [Phys. Rev. E 88, 022127 (2013)].

This corrects the article DOI: 10.1103/PhysRevE.88.022127.

Molecules with an induced dipole moment in a stochastic electric field.

The mean-field dynamics of a molecule with an induced dipole moment (e.g., a homonuclear diatomic molecule) in a deterministic and a stochastic (fluctuating) electric field is solved to obtain the decoherence properties of the system. The average (over fluctuations) electric dipole moment and average angular momentum as a function of time for a Gaussian white noise electric field are determined via perturbative and nonperturbative solutions in the fluctuating field. In the perturbative solution, 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 electric field. This is in contrast to the decay of the average over fluctuations of a magnetic moment in a Gaussian white noise magnetic field. In the nonperturbative solution, the component of the average electric dipole moment and the average angular momentum in the deterministic electric field direction also decay to zero.

Feshbach resonance without a closed-channel bound state.

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 interchannel coupling, Feshbach resonance can occur even when the closed channel does not have a bound state. This may extend the range of ultracold 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 ε-ε(B), where ε is the scattering energy and ε(B) is the bound-state energy in the closed channel (when there is one).

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 momentum 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 electric 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.

Spin decoherence due to fluctuating fields.

The dynamics of a spin in the presence of a deterministic and a fluctuating magnetic field is solved for analytically to obtain the averaged value of the spin as a function of time for various kinds of fluctuations (noise). Specifically, analytic results are obtained for the time dependence of the expectation value of the spin, averaged over fluctuations, for Gaussian white noise, Gaussian colored noise, and non-Gaussian telegraph noise. Fluctuations cause the decay of the average spin vector (decoherence). For noise with a finite temporal correlation time, a deterministic component of the field can suppress the decoherence of the spin component along the field. Hence, decoherence can be manipulated by controlling the deterministic magnetic field. A simple universal physical picture emerges which explains the mechanism for the suppression of decay.

Creating very slow optical gap solitons with a grating-assisted coupler.

We show that optical gap solitons can be produced with velocities down to 4% of the group velocity of light using a grating-assisted coupler, i.e., a fiber Bragg grating that is linearly coupled to a non-Bragg fiber over a finite domain. Forward- and backward-moving light pulses in the non-Bragg fiber(s) that reach the coupling region simultaneously couple into the Bragg fiber and form a moving soliton, which then propagates beyond the coupling region. Two of these solitons can collide to create an even slower or stopped soliton.

Interference of Bose-Einstein condensates.

A formalism for describing the coherence and interference properties of two atomic clouds of Bose-Einstein condensates (BEC) is presented, which is applicable even in the opposite limits when the BEC clouds are initially coherent and when they are initially independent. First, we develop a mean-field theory wherein one mean-field mode is used, and then, for fragmented (i.e., independent) condensates, we use a mean-field theory with two modes. We then develop a full two-mode field theory, with a field operator composed of a sum of two terms containing matter wave mode functions phi1 and phi2, that multiply the destruction operators of the modes, a1 and a2. When atom-atom interactions are present and when the mode functions overlap, the matter wave mode functions phi1 and phi2 develop components moving to the right and left, and this results in interference fringes in the density. At the many-body level, another source of interference arises from expectation values of the form (a(i)+a(j)) with i double dagger j, which become nonzero due to tunneling and interactions. We detail how these two sources of interference affect the density profile and the density-density correlation functions of Bose-Einstein condensates in the coherent and in the fragmented regimes.

Optoacoustic solitons in Bragg gratings.

Optical gap solitons, which exist due to a balance of nonlinearity and dispersion due to a Bragg grating, can couple to acoustic waves through electrostriction. This gives rise to a new species of "gap-acoustic" solitons (GASs), for which we find exact analytic solutions. The GAS consists of an optical pulse similar to the optical gap soliton, dressed by an accompanying phonon pulse. Close to the speed of sound, the phonon component is large. In subsonic (supersonic) solitons, the phonon pulse is a positive (negative) density variation. Coupling to the acoustic field damps the solitons' oscillatory instability, and gives rise to a distinct instability for supersonic solitons, which may make the GAS decelerate and change direction, ultimately making the soliton subsonic.

Nonlinear adiabatic passage from fermion atoms to boson molecules.

We study the dynamics of an adiabatic sweep through a Feshbach resonance in a quantum gas of fermionic atoms. Analysis of the dynamical equations, supported by mean-field and many-body numerical results, shows that the dependence of the remaining atomic fraction Gamma on the sweep rate alpha varies from exponential Landau-Zener behavior for a single pair of particles to a power-law dependence for large particle number N. The power law is linear, Gamma is proportional to alpha, when the initial molecular fraction is smaller than the 1/N quantum fluctuations, and Gamma is proportional to alpha(1/3) when it is larger. Experimental data agree well with a linear dependence, but do not conclusively rule out the Landau-Zener model.

Gap solitons in a medium with third-harmonic generation.

We find two-component optical solitons in a nonlinear waveguide with a Bragg grating, including Kerr effects and third-harmonic generation (THG). The model may be realized in temporal and in spatial domains. Two species of fundamental gap solitons (GSs) are found. The first ("THG-gap soliton") has the bulk of its energy at the fundamental frequency (FF) and a lesser part in the third-harmonic (TH) band. The FF part of the soliton is always single humped; the TH part may be single or double humped. Stability domains for quiescent and moving THG-gap solitons strongly shrink with increase of velocity. The second species is the usual ("simple") GS, sitting entirely in the TH band. More complex solutions are also found, in the form of a bound state of a THG-gap soliton and two simple GSs, with a finite binding energy. When a THG-gap soliton is unstable, the instability is oscillatory. It may ultimately cause the THG-gap soliton to throw off some radiation and evolve into a localized structure with the FF and TH components out of phase, with or without internal oscillations. Stable solitons feature an excited state (i.e., they support a localized eigenmode).

Conversion efficiency of ultracold fermionic atoms to bosonic molecules via Feshbach resonance sweep experiments.

We explain why the experimental efficiency observed in the conversion of ultracold Fermi gases of 40K and 6Li atoms into diatomic Bose gases is limited to 0.5 when the Feshbach resonance sweep rate is sufficiently slow to pass adiabatically through the Landau-Zener transition but faster than "the collision rate" in the gas, and increases beyond 0.5 when it is slower. The 0.5 efficiency limit is due to the preparation of a statistical mixture of two spin states, required to enable s-wave scattering. By constructing the many-body state of the system we show that this preparation yields a mixture of even and odd parity pair states, where only even parity can produce molecules. The odd parity spin-symmetric states must decorrelate before the constituent atoms can further Feshbach scatter, thereby increasing the conversion efficiency; "the collision rate" is the pair decorrelation rate.

Near-field and far-field propagation of beams and pulses in dispersive media.

We formulate an efficient exact method of propagating optical wave packets (and cw beams) in isotropic and nonisotropic dispersive media. The method does not make the slowly varying envelope approximation in time or space and treats dispersion and diffraction exactly to all orders, even in the near field. It can also be used to determine the partial differential wave equation for pulses (and beams) to any order as a power series in the partial derivatives with respect to time and space. The method can treat extremely focused pulses and beams, e.g., from near-field scanning optical microscopy sources whose transverse spatial extent in smaller than a wavelength.

Increased efficiency for sum-frequency generation for broadband input fields.

A new method of efficient sum-frequency generation for broadband input fields is theoretically analyzed and experimentally demonstrated. The method involves using an arrangement with two or more nonlinear mixing crystals, with a time-delay line situated between the crystals, for one of the fundamental fields relative to the other. The delay line temporally shifts the fundamental fields, one relative to another, by a time longer than their coherence time. The improvement in efficiency for sum-frequency generation using this method is much higher than for difference-frequency generation.

Theory of mode-locked intracavity second-harmonic generation in a ring laser.

We model the dynamics of a Q-switched mode-locked intracavity second-harmonic-generation (SHG) ring laser. Numerical studies show that a long train of constant-pulse-duration short pulses at the second-harmonic and fundamental frequencies result. The efficiency of the mode-locked intracavity SHG laser is comparable with that of the mode-locked fundamental-frequency laser not containing SHG.

Birefringence of solid-state laser media: broadband tuning discontinuities and application to laser line narrowing.

Spectral consequences that result from using birefringent media with broadband gain inside of laser cavities containing polarizing elements are described. We show that the laser intensity is modulated as a function of the output frequency unless the cavity elements are carefully aligned so that their polarization axis coincides with a principal optical axis of the gain medium. Analysis of the tuning characteristics of a birefringent polarizationdependent gain medium is exploited to provide a simple method for line narrowing the laser output. By introduction of an intracavity birefringent compensator the narrow-band output can be continuously tuned. Experimental results for alexandrite lasers are presented.

Thermodynamic bound on the phase-conjugate correction of optical distortions.

We show that there is a limit to the maximum efficiency achievable for correcting optical distortion (beam healing) using phase conjugation. This limit is quantum thermodynamic and stems from the impossibility of reducing the beam entropy by a lossless retrace of the phase aberrator.