Spin squeezing in a bimodal condensate: spatial dynamics and particle losses

We propose an analytical method to study the entangled spatial and spin dynamics of interacting bimodal Bose-Einstein condensates. We show that at particular times during the evolution spatial and spin dynamics disentangle and the spin squeezing can be predicted by a simple two-mode model. We calculate the maximum spin squeezing achievable in experimentally relevant situations with Sodium or Rubidium bimodal condensates, including the effect of the dynamics and of one, two and three-body losses.     

A systematic elimination procedure for Ito stochastic differential equations and the adiabatic approximation

We study a class of nonlinear Ito stochastic differential equations (with possibly state dependent diffusion coefficients), in which the variables can be divided into linearly damped (slaved) variables s and linearly undamped variablesu (order parameters). We devise a systematic and constructive procedure to eliminate the slaved variables. We take explicit time and chance dependence of the slaved variables into account, the latter via a family of diffusion processesZ _t ^(v) . These act as fluctuating coefficients of the Center Manifolds _t=s(u _t, t,Z _t ^(v) (v=2, 3, ...)) and appear explicitly in the elimination procedure. We show how in the Ito calculus fluctuating and deterministic coefficients of the Center Manifold are more completely separated than in the previously treated Stratonovich case [1]. The adiabatic approximation is defined as a partial summation of the elimination expansion and the stochastic generalization ofs=0 is derived. We show how thus ambiguity of stochastic calculi is removed. Closed form summations are given in two examples. We briefly indicate the potential use of perturbation theory techniques in the systematic elimination procedure.     

On the physical interpretation of Heywood and Redhead's algebraic impossibility theorem

Heywood and Redhead's 1983 algebraic (Kochen-Specker type) impossibility proof, which establishes the inconsistency of a broad class of contextualized local realistic theories, assumes two locality conditions and two auxiliary assumptions. One of those auxiliary conditions, FUNC^*, has been called a physically unmotivated,ad hoc formal constraint.In this paper, we derive Heywood and Redhead's auxiliary conditions from physical assumptions. This allows us to analyze which classes of hidden-variables theories escape the Heywood-Redhead contradiction. By doing so, we hope to clarify the physical and philosophical ramifications of the Heywood-Redhead proof. Most current hidden-variables theories, it turns out, violate Heywood and Redhead's auxiliary conditions.1. See Redhead [1], pp. 133–136, for a complete discussion.2. Arthur Fine first pointed out the implicit reliance on FUNC^*, and proved FUNC^* to be both consistent with and independent of the Value Rule.3. LetA=_ia_i P _i andB=_jb_j P_j be spectral resolutions ofA andB. Then <A,B> is the observable associated with maximal operatorR=_ijf_ij P _iP_j, where f_ij=F(a_i,b_j), and where function F is 1:1.4. Heywood and Redhead's versions of these conditions employ equivalence-class notation to specify the ontological context. {<D,E>}={R} refers to the equivalence class of all possible <D,E> formed by using different F functions (cf. Footnote 3). Clearly, such notation assumes that ifR andR are two distinct commuting maximal operators formed as described in Fn. 3 fromD andE using two different F(d_i,e_j) functions, then [Q]^t _(R)(R)=[Q]^t _(R)(R), so that [Q]^t _{R}(R) is uniquely defined.Heywood and Redhead never rely upon this assumption in their proof, however. It is easily checked that a Heywood-Redhead contradiction follows from my non-equivalence class versions of OLOC, ELOC, VR, and FUNC^*. Therefore, I will not use equivalence class notation.5. Here I denote by µ_R the composite state of all the apparatuses needed to measure R. So µ_R may represent the state of more than one device.6 This is because in a hidden-variables framework, quantum mechanical probabilities are a weighted average of the underlying hidden-variables probabilities.7. This argument resembles a proof given by Fine [8].8. Recall from theorem 1 that ifQ=f(R), then for all quantum states , P_(t)(Qf(r), R=r)=0.     

Expansion dynamics of an array of high density Bose-Einstein condensates produced in a 1D CO<Subscript>2</Subscript> laser optical lattice

We discuss the expansion dynamics under mean-field repulsion of an array of ⁸⁷Rb Bose-Einstein condensates produced in an all-optical scheme involving 1D lattice with nearly 10⁵ atoms, after fast evaporative cooling of just about 1 s. Single site occupation exceeds 2 × 10⁴ in our experiments. The possibility of transition to two-dimensionality was also investigated. The expansion behavior of the high density multiple micro-condensates produced directly in the CO₂ laser 1D optical lattice, with a lattice spacing of 5.3 μm, agrees well with a numerical simulation based on the mean-field theory.     

Build-up of coherence between initially-independent subsystems: The case of Bose-Einstein condensates

When initially-independent subsystems are made to contact, coherence can develop due to interaction between them. We exemplify and demonstrate this paradigm through several scenarios of two initially-independent Bose-Einstein condensates which are allowed to collide. The build-up of coherence depends strongly on time, interaction strength and other parameters of each condensate. Implications are discussed.     

Delay times for symmetrized and antisymmetrized quantum tunneling configurations

The quartic confining potential has emerged as a key ingredient to obtain fast rotating vortices in BEC as well as observation of quantum phase transitions in optical lattices. We calculate the critical temperature T_c of bosons at which normal to BEC transition occurs for the quartic confining potential. Further more, we evaluate the effect of finite particle number on T_c and find that ΔT_c/T_c is larger in quartic potential as compared to quadratic potential for number of particles <10⁵. Interestingly, the situation is reversed if the number of particles is 10⁵.     

The evolution of magnetic,electrical and structural properties of nanogranular [FeCoBN/SiN]×n thin films

Some results concerning the magnetic, electrical and microstructural properties of multilayer [FeCoBN/Si₃N₄]×n films in view of their utilization for manufacturing thin film magnetic inductors are presented. A comparison between the magnetic, electrical and structural properties of FeCoBN and [FeCoBN/Si₃N₄]×n thin films is also reported. The [FeCoBN/Si₃N₄]×n thin films with the thickness of the FeCoBN layers varied from 10 to 30 nm, exhibit good soft magnetic characteristics and high values for electrical resistivity such as Ms of 172–185 A m²/kg, Hc of 318–1433 A/m and ρ of 82–48×10⁻⁷ Ω m, respectively. These physical properties of the samples are discussed in relation with the microstructure of the multilayer system.     

Measurement of the quadratic Zeeman shift of Rb hyperfine sublevels using stimulated Raman transitions

We demonstrate a technique for directly measuring the quadratic Zeeman shift using stimulated Raman transitions. The quadratic Zeeman shift has been measured yielding Δν=1296.8±3.3 Hz/G² for magnetically insensitive sublevels (5S_1/2,F=2,m_F=0→5S_1/2,F=3,m_F=0) of ⁸⁵Rb by compensating the magnetic field and cancelling the ac Stark shift. We also measured the cancellation ratio of the differential ac Stark shift due to the imbalanced Raman beams by using two pairs of Raman beams (σ⁺, σ⁺) and it is 1:3.67 when the one-photon detuning is 1.5 GHz in the experiment.     

Metastable state and macroscopic quantum tunneling of binary mixtures

We provide a mixing model to explore the metastable state and the macroscopic quantum tunneling (MQT) of binary mixtures. For , we first observe the two condensates form the symmetry-breaking state (SBS) and then suddenly transfer to the symmetry-preserving state (SPS) through the MQT. The SBS is shown to be the metastable state in our system. We find the MQT does not spontaneously arise. The inducement mechanism is the damping but not the excitations. The damping mechanism can also control the lifetime and the tunneling decay rate of the SBS. Finally, we further present the origin of these phenomena by examining the energy of the system.     

Schwinger mechanism for gluon-pair production in the presence of arbitrary time-dependent chromo-electric field

We study the Schwinger mechanism for gluon-pair production in the presence of an arbitrary time-dependent chromo-electric background field E ^a (t) with arbitrary color index a=1,2,…,8 in SU(3) by directly evaluating the path integral. We obtain an exact expression for the probability of non-perturbative gluon-pair production per unit time per unit volume and per unit transverse momentum, , from arbitrary E ^a (t). We show that the tadpole (or single-gluon) effective action does not contribute to the non-perturbative gluon-pair production rate, . We find that the exact result for non-perturbative gluon-pair production is independent of all the time derivatives , where n=1,2,…,∞, and that it has the same functional dependence on the two Casimir invariants, [E ^a (t)E ^a (t)] and [d _abc E ^a (t)E ^b (t)E ^c (t)]², as the constant chromo-electric field E ^a result with the replacement: E ^a →E ^a (t). This result relies crucially on the validity of the shift conjecture, which has not yet been established. This result may be relevant to the study of the production of a non-perturbative quark–gluon plasma at RHIC and LHC.     

Josephson oscillation of a superfluid Fermi gas

Using the complete numerical solution of a time-dependent three-dimensional mean-field model we study the Josephson oscillation of a superfluid Fermi gas (SFG) at zero temperature formed in a combined axially-symmetric harmonic plus one-dimensional periodic optical-lattice (OL) potentials after displacing the harmonic trap along the axial OL axis. We study the dependence of Josephson frequency on the strength of the OL potential. The Josephson frequency decreases with increasing strength as found in the experiment of Cataliotti et al. [Science 293, 843 (2001)] for a Bose-Einstein condensate and of the experiment of Pezzè et al. [Phys. Rev. Lett. 93, 120401 (2004)] for an ideal Fermi gas. We demonstrate a breakdown of Josephson oscillation in the SFG for a large displacement of the harmonic trap. These features of Josephson oscillation of a SFG can be tested experimentally.     

Bose-Einstein Condensates in a One-Dimensional Optical Lattice: from Superfluidity to Number-Squeezed States

We study the phase coherence property of Bose-Einstein condensates confined in a one-dimensional optical lattice formed by a standing-wave laser field. The lattice depth is determined using a method of Kapitza-Dirac scattering between a condensate and a short pulse lattice potential. Condensates are then adiabatically loaded into the optical lattice. The phase coherence property of the confined condensates is reflected by the interference patterns of the expanded atomic cloud released from the optical lattice. For weak lattice, nearly all of the atoms stay in a superfluid state. However, as the lattice depth is increased, the phase coherence of the whole condensate sample is gradually lost, which confirms that the sub-condensates in each lattice well have evolved into number-squeezed states.     

Effective one-dimensional dynamics of elongated Bose-Einstein condensates

By using a variational approach in combination with the adiabatic approximation we derive a new effective 1D equation of motion for the axial dynamics of elongated condensates. For condensates with vorticity ∣q∣ = 0 or 1, this equation coincides with our previous proposal [A. Muñoz Mateo, V. Delgado, Phys. Rev. A 77 (2008) 013617]. We also rederive the nonpolynomial Schrödinger equation (NPSE) in terms of the adiabatic approximation. This provides a unified treatment for obtaining the different effective equations and allows appreciating clearly the differences and similarities between the various proposals. We also obtain an expression for the axial healing length of cigar-shaped condensates and show that, in the local density approximation and in units of the axial oscillator length, it coincides with the inverse of the condensate axial half-length. From this result it immediately follows the necessary condition for the validity of the local density approximation. Finally, we obtain analytical formulas that give the frequency of the axial breathing mode with accuracy better than 1%. These formulas can be relevant from an experimental point of view since they can be expressed in terms only of the axial half-length and remain valid in the crossover between the Thomas-Fermi and the quasi-1D mean-field regimes. We have corroborated the validity of our results by numerically solving the full 3D Gross-Pitaevskii equation.     

Vortex structure of Gross-Pitaevskii model

The vortex line of the Gross-Pitaevskii model is studied. The kinetic helicity of the vortex is discussed, and vortex structure is classified by the Hopf index, linking number in geometry. A mechanism of generation and annihilation of vortex lines is given by the method of phase singularity theory. The dynamic behavior of the vortex at the critical points is discussed in detail, and three kinds of length approximation relations at the neighborhood of a critical point are given: l ∝ (t − t^∗)^1/2, l ∝ t − t^∗, l = const.     

Monte Carlo wavefunction approach to the dissipative quantum-phase dynamics of two-component Bose-Einstein condensates

We investigate the relaxation effects on the dynamics of two-component dilute gas Bose-Einstein condensates (BEC) with relatively different two-body interactions and Josephson couplings between the two components. Three types of relaxation effects, i.e., one- and three-body losses and a pure phase relaxation caused by elastic two-body collision between condensed and noncondensed atoms, are examined on the dynamical behavior of a macroscopic superposition, i.e., Schr?dinger cat state, of two states with atom-number differences between the two components, which is known to be created by the time evolution in certain parameter regimes. Although three-body losses show a relatively large suppression of the revival behavior of Schr?dinger cat state and the Pegg-Barnett phase-difference distribution between the two components for a small-size Schr?dinger cat state, one- and three-body loss effects are not shown to directly depend on the size of Schr?dinger cat state. In contrast, the pure-phase relaxation effects, causing a reduction of phase-difference distribution and then decaying the Schr?dinger cat state, significantly increase with the increase of the size of Schr?dinger cat state. These features suggest that a detection of damped collapse-revival behavior is highly possible for medium-size Schr?dinger cat states in small-size two-component BECs.     

Separation of the ortho and para NMR signals in solid deuterium via DQ filtering

Double quantum (DQ) filtering is shown to lead to an effective separation of the NMR signals from the para (I = 1) and ortho (I = 2) molecules in solid deuterium. The separation is achieved by the pulse sequence 90_φ^°–t_pr–90_φ^°–t_ev–90_x^°–t, where the phase-cycled first two pulses create the DQ coherence. Two components are observed after the third pulse; the para signal shows the maximum at a short time t while the ortho signal reaches the maximum at a longer t. The observed signal can be expressed as ∑_I [F_I(t_pr − t) − F_I(t_pr + t)], where F_I(t) is a proper fitting function for the free induction signal of the para and ortho molecules (with I = 1 or 2, respectively). Numerical fits to experimental data at 4.2 and 2 K show that this method can be used to determine the ratio F₁(0)/F₂(0) and thus, because the initial value F_I(0) is proportional to the respective magnetization before the pulse sequence, the ortho and para concentrations in solid deuterium.     

Dynamics of isolated twin boundary in (TMTSF)

Intermittent and irregular motion of isolated twin boundary (kink) in organic crystal (TMTSF)₂PF₆ was studied at room temperature. Both the local velocity and the time of intermission are determined not only by external stress and temperature but also by the time (t w) elapsed after the backward passage and before the following forward one. When the kink moves after longer t w, its velocity becomes smaller and the time of intermission longer. Both tend to saturate for t w longer than 10² s. This result indicates that some disorder is induced in the lattice by the backward motion and it is relaxed during t w. We also found that the effect of the backward motion of one kink on its following motion is equivalent quantitatively to that of the forward motion of the pair-created counterpart. Received: 14 April 1998 / Received in final form and Accepted: 1st September 1998     

Single α-particle orbits and Bose-Einstein condensation in <Superscript>12</Superscript>C

Bosonic properties of α particles such as single-α orbits and occupation numbers in J^π = 0⁺, 2⁺, 1^- and 3^- states of ¹²C around the 3α threshold are investigated with the semi-microscopic 3α cluster model. As in other studies, we found that the 0⁺₂ (2⁺₂) state has dilute-3α-condensate-like structure in which the α particle is occupied in the single S (D) orbit with about 70% (80%) probability. The radial behaviors of the single-α orbits as well as the occupation numbers are discussed in detail in comparison with those for the 0⁺₁ and 2⁺₁ states together with the 1^-₁ and 3^-₁ states.     

Propagation of electromagnetic waves generated by moving sources in dispersive media

The propagation of electromagnetic waves issued by modulated moving sources of the form j( t,x ) = a( t )e ^{- iw₀ t} [(x)\dot]₀ ( t )d( x - x₀ ( t ) )j\left( {t,x} \right) = a\left( t \right)e^{ - i\omega _0 t} \dot x_0 \left( t \right)\delta \left( {x - x_0 \left( t \right)} \right) is considered, where j(t, x) stands for the current density vector, x = (x ₁, x ₂, x ₃) ∈ ℝ³ for the space variables, t ∈ ℝ for time, t → x ₀(t) ∈ ℝ³ for the vector function defining the motion of the source, ω ₀ for the eigenfrequency of the source, a(t) for a narrow-band amplitude, and δ for the standard δ function. Suppose that the media under consideration are dispersive. This means that the electric and magnetic permittivity ɛ(ω), μ(ω) depends on the frequency ω. We obtain a representation of electromagnetic fields in the form of time-frequency oscillating integrals whose phase contains a large parameter λ > 0 characterizing the slowness of the change of the amplitude a(t) and the velocity [(x)\dot]₀ ( t )\dot x_0 \left( t \right) and a large distance between positions of the source and the receiver. Applying the two-dimensional stationary phase method to the integrals, we obtain explicit formulas for the electromagnetic field and for the Doppler effects. As an application of our approach, we consider the propagation of electromagnetic waves produced by moving source in a cold nonmagnetized plasma and the Cherenkov radiation in dispersive media.