arXiv subjects
Publications and source records attributed to S. E. Skipetrov.
We study correlations of atomic density in a weakly interacting Bose-Einstein condensate, expanding diffusively in a random potential. We show that these correlations are long-range and that they are strongly enhanced at long times. Density at distant points exhibits negative correlations.
We study the effect of Anderson localization on the expansion of a Bose-Einstein condensate, released from a harmonic trap, in a 3D random potential. We use scaling arguments and the self-consistent theory of localization to show that the long-time behavior of the condensate density is controlled by a single parameter equal to the ratio of the mobility edge and the chemical potential of the condensate. We find that the two critical exponents of the localization transition determine the evolution of the condensate density in time and space.
We present a microscopic derivation of self-consistent equations of Anderson localization in a disordered medium of finite size. The derivation leads to a renormalized, position-dependent diffusion coefficient. The position dependence of the latter is due to the position dependence of return probability in a bounded medium.
The heat capacity $C_{p}$ of an array of independent aluminum rings has been measured under an external magnetic field $\vec{H}$ using highly sensitive ac-calorimetry based on a silicon membrane sensor. Each superconducting vortex entrance induces a phase transition and a heat capacity jump and hence $C_{p}$ oscillates with $\vec{H}$. This oscillatory and non-stationary behaviour measured versus the magnetic field has been studied using the Wigner-Ville distribution (a time-frequency representation). It is found that the periodicity of the heat capacity oscillations varies significantly with the magnetic field; the evolution of the period also depends on the sweeping direction of the field. This can be attributed to a different behavior between expulsion and penetration of vortices into the rings. A variation of more than 15% of the periodicity of the heat capacity jumps is observed as the magnetic field is varied. A description of this phenomenon is given using an analytical solution of the Ginzburg-Landau equations of superconductivity.
We formulate a quantum theory of dynamic multiple light scattering in fluctuating disordered media and calculate the fluctuation and the autocorrelation function of photon number operator for light transmitted through a disordered slab. The effect of disorder on the information capacity of a quantum communication channel operating in a disordered environment is estimated and the use of squeezed light in diffusing-wave spectroscopy is discussed.
We report the first observation of the impact of mesoscopic fluctuations on the photocount statistics of coherent light scattered in a random medium. Poisson photocount distribution of the incident light widens and gains additional asymmetry upon transmission through a suspension of small dielectric spheres. The effect is only appreciable when the average number of photocounts becomes comparable or larger than the effective dimensionless conductance g of the sample.
We establish a conceptual relation between the fluctuations of the local density of states (LDOS) and intensity correlations in speckle patterns resulting from multiple scattering of waves in random media. We show that among known types of speckle correlations (C1, C2, C3, and C0) only C0 contributes to LDOS fluctuations in the infinite medium. We propose to exploit the equivalence of LDOS fluctuations and C0 intensity correlation as a `selection rule' for scattering processes contributing to C0.
We report highly sensitive specific heat measurement on mesoscopic superconducting loops at low temperature. These mesoscopic systems exhibit thermal properties significantly different from that of the bulk materials. The measurement is performed on a silicon membrane sensor where 450 000 superconducting aluminium loops are deposited through electron beam lithography under an applied magnetic field. Each entry of a vortex is associated to a jump in the specific heat of few thousands of Boltzmann constant kB indicating the existence of phase transitions. The periodicity of this sequential phase transitions is a nontrivial behaviour and varies strongly as the temperature is decreased. The successive phase transitions are well described by the Ginzburg-Landau theory of superconductivity. The presence of metastable states is responsible for the n-0 (n=1, 2, 3...) periodicity of the discontinuities of the measured specific heat.
We develop a self-consistent theoretical approach to the dynamics of Anderson localization in open three-dimensional (3D) disordered media. The approach allows us to study time-dependent transmission and reflection, and the distribution of decay rates of quasi-modes of 3D disordered slabs near the Anderson mobility edge.
We consider the phenomenon of weak localization of a short wave pulse in a quasi-1D disordered waveguide. We show that the long-time decay of the average transmission coefficient is not purely exponential, in contradiction with predictions of the diffusion theory. The diffusion theory breaks down completely for times exceeding the Heisenberg time. We also study the survival probability of a quantum particle in a disordered waveguide and compare our results with previous calculations using the super-symmetric nonlinear sigma model.
We report the first experimental evidence of nontrivial thermal behavior of the simplest mesoscopic system - a superconducting loop. By measuring the specific heat C of an array of 450,000 noninteracting aluminum loops with very high accuracy of ~20 fJ/K, we show that the loops go through a periodic sequence of phase transitions (with period of an integer number of magnetic flux quanta) as the magnetic flux threading each loop is increased. The transitions are well described by the Ginzburg-Landau theory and are accompanied by discontinuities of C of only several thousands of Boltzmann constants k_B.
We study the temporal evolution of speckle patterns in transmission of short wave pulses through a disordered waveguide. In the diffuse regime, the short-range spatial structure of speckles is the same as for continuous wave (cw) illumination, whereas the long-range correlation between distant speckle spots grows linearly with time and can exceed its cw value. We discuss the physical origin of this phenomenon, compare our results to recent microwave experiments, and suggest that a similar linear growth with time should also be characteristic for other mesoscopic interference phenomena.
We develop a transport theory to describe the dynamics of (weakly) localized waves in a quasi-1D tube geometry both in reflection and in transmission. We compare our results to recent experiments with microwaves, and to other theories such as random matrix theory and supersymmetric theory.
We study the second harmonic generation (SHG) in a suspension of small spherical particles confined within a slab, assuming undepleted pump and applying (i) single scattering approximation and (ii) diffusion approximation. In the case (i), the angular diagram, the differential and total crossections of the SHG process, as well as the average cosine of SH scattering angle are calculated. In the case (ii), the average SH intensity is found to show no explicit dependence on the linear scattering properties of the suspension. The average intensity of SH wave scales as I_0 L / Λ_2 in both cases (i) and (ii), where I_0 is the intensity of the incident wave, L is the slab thickness, and Λ_2 is an intensity-dependent "SH scattering" length.
Linear stability analysis of speckle pattern resulting from multiple, diffuse scattering of coherent light waves in random media with intensity-dependent refractive index (noninstantaneous Kerr nonlinearity) is performed. The speckle pattern is shown to become unstable with respect to dynamic perturbations within a certain frequency band, provided that nonlinearity exceeds some frequency-dependent threshold. Although the absolute instability threshold is independent of the response time of nonlinearity, the latter significantly affects speckle dynamics (in particular, its spectral content) beyond the threshold. Our results suggest that speckle dynamics becomes chaotic immediately beyond the threshold.
We review our recent theoretical results on multiple scattering of waves in nonlinear disordered media. In particular, we discuss angular correlations of scattered waves, coherent backscattering cone, and the new phenomenon of temporal instability of multiply scattered waves in disordered media with sufficiently strong nonlinearity. Instability threshlod is derived, dynamics of speckle pattern beyond the threshold is discussed.
Onset of the instability of a multiple-scattering speckle pattern in a random medium with Kerr nonlinearity is significantly affected by the noninstantaneous character of the nonlinear medium response. The fundamental time scale of the spontaneous speckle dynamics beyond the instability threshold is set by the largest of times $T_{\mathrm{D}}$ and $τ_{\mathrm{NL}}$, where $T_{\mathrm{D}}$ is the time required for the multiple-scattered waves to propagate through the random sample and $τ_{\mathrm{NL}}$ is the relaxation time of the nonlinearity. Inertial nature of the nonlinearity should complicate the experimental observation of the instability phenomenon.
We consider the information content h of a scalar multiple-scattered, diffuse wave field $ψ(\vec{r})$ and the information capacity C of a communication channel that employs diffuse waves to transfer the information through a disordered medium. Both h and C are shown to be directly related to the mesoscopic correlations between the values of $ψ(\vec{r})$ at different positions $\vec{r}$ in space, arising due to the coherent nature of the wave. For the particular case of a communication channel between two identical linear arrays of $n \gg 1$ equally-spaced transmitters/receivers (receiver spacing a), we show that the average capacity $ \propto n$ and obtain explicit analytic expressions for $ /n$ in the limit of $n \to \infty$ and $k \ell \to \infty$, where $k= 2π/ λ$, $λ$ is the wavelength, and $\ell$ is the mean free path. Modification of the above results in the case of finite but large n and $k \ell$ is discussed as well.