Coexistence of superfluid and Mott phases of lattice bosons

Recent experiments on strongly-interacting bosons in optical lattices have revealed the co-existence of spatially-separated Mott-insulating and number-fluctuating phases. The description of this inhomogeneous situation is the topic of this Letter. We establish that the number-fluctuating phase forms a superfluid trapped between the Mott-insulating regions and derive the associated collective mode structure. We discuss the interlayer's crossover between two- and three-dimensional behavior as a function of the lattice parameters and estimate the critical temperatures for the transition of the superfluid phase to a normal phase

Time evolution of Matrix Product States

In this work we develop several new simulation algorithms for 1D many-body quantum mechanical systems combining the Matrix Product State variational ansatz with Taylor, Pade and Arnoldi approximations to the evolution operator. By comparing all methods with previous techniques based on Trotter decompositions we demonstrate that the Arnoldi method is the best one, reaching extremely good accuracy with moderate resources. Finally we apply this algorithm to studying the formation of molecules in an optical lattices when crossing a Feschbach resonance with a cloud of two-species hard-core bosons.Comment: More extensive comparison with all nearest-neighbor spin s=1/2 models. The results in this manuscript have been superseded by a more complete work in cond-mat/061021

Adiabatic perturbation theory: from Landau-Zener problem to quenching through a quantum critical point

We discuss the application of the adiabatic perturbation theory to analyze the dynamics in various systems in the limit of slow parametric changes of the Hamiltonian. We first consider a two-level system and give an elementary derivation of the asymptotics of the transition probability when the tuning parameter slowly changes in the finite range. Then we apply this perturbation theory to many-particle systems with low energy spectrum characterized by quasiparticle excitations. Within this approach we derive the scaling of various quantities such as the density of generated defects, entropy and energy. We discuss the applications of this approach to a specific situation where the system crosses a quantum critical point. We also show the connection between adiabatic and sudden quenches near a quantum phase transitions and discuss the effects of quasiparticle statistics on slow and sudden quenches at finite temperatures.Comment: 20 pages, 3 figures, contribution to "Quantum Quenching, Annealing and Computation", Eds. A. Das, A. Chandra and B. K. Chakrabarti, Lect. Notes in Phys., Springer, Heidelberg (2009, to be published), reference correcte

Paramagnetic centers in amorphous and microcrystalline silicon irradiated with 2 МeV electrons

Amorphous and microcrystalline silicon are well known materials for thin film large area electronics. The defects in the material are an important issue for the device quality and the manufacturing process optimization. We study defects in thin film silicon with electron spin resonance (ESR). In order to vary the defect density in a wide range 2 MeV electron bombardment at 100 K was applied with dose as high as 10¹⁸ e*cm⁻². Samples were investigated after deposition, after irradiation and between the annealing steps. The spin density (Ns) in the material was varied over 3 orders of magnitude. Strong satellites with g≈2.010 and g≈2.000 were observed on the shoulders of the dangling bond line. The initial Ns and the shape of the resonance line were restored after annealing.Аморфний і мікрокристалічний кремній є широко відомими матеріалами для виробництва тонкоплівкової електроники великої площі. Дефекти у даних матеріалах відіграють вирішальну роль для якості пристроїв і оптимізації виробничих процесів. Ми досліджували тонкоплівковий гідрогенований кремній методом вимірів електронного парамагнитного резонансу (ЕПР). Для зміни щільності дефектів у широкому диапазоні зразки було опромінено електронами з енергією 2 МеВ. Зразки було досліджено після осадження, після опромінення і між етапами відпалу. Щільність спинів (Ns) в матеріалі змінювалась в межах 3-х порядків величини. З обох боків від центрального резонансу, що характеризує обірвані зв’язки кремнію, спостеригались потужні додаткові резонансні лінії (g≈2.010 и g≈2.000). Після відпалу форма резонансних ліній і щільність спинів поверталися до вихідних показників.Аморфный и микрокристаллический кремний являются широко известными материалами для производства тонкопленочной электроники большой площади. Дефекты в данных материалах играют решающую роль для качества приборов и оптимизации производственных процессов. Мы исследовали тонкопленочный гидрогенированный кремний методом измерений электронного парамагнитного резонанса (ЭПР). Для изменения плотности дефектов в широких пределах образцы облучались электронами с энергией 2 МэВ. Образцы исследовались после осаждения, после облучения и между стадиями отжига. Плотность спинов (Ns) в материале изменялась в пределах 3-х порядков величины. По обе стороны от центрального резонанса, характеризующего оборванные связи кремния, наблюдались мощные дополнительные резонансные линии (g≈2.010 и g≈2.000). После отжига форма резонансных линий и плотность спинов возвращались к исходным значениям

Quantum quenches from integrability: the fermionic pairing model

Understanding the non-equilibrium dynamics of extended quantum systems after the trigger of a sudden, global perturbation (quench) represents a daunting challenge, especially in the presence of interactions. The main difficulties stem from both the vanishing time scale of the quench event, which can thus create arbitrarily high energy modes, and its non-local nature, which curtails the utility of local excitation bases. We here show that nonperturbative methods based on integrability can prove sufficiently powerful to completely characterize quantum quenches: we illustrate this using a model of fermions with pairing interactions (Richardson's model). The effects of simple (and multiple) quenches on the dynamics of various important observables are discussed. Many of the features we find are expected to be universal to all kinds of quench situations in atomic physics and condensed matter.Comment: 10 pages, 7 figure

Symmetric-Asymmetric transition in mixtures of Bose-Einstein condensates

We propose a new kind of quantum phase transition in phase separated mixtures of Bose-Einstein condensates. In this transition, the distribution of the two components changes from a symmetric to an asymmetric shape. We discuss the nature of the phase transition, the role of interface tension and the phase diagram. The symmetric to asymmetric transition is the simplest quantum phase transition that one can imagine. Careful study of this problem should provide us new insight into this burgeoning field of discovery.Comment: 6 pages, 3 eps figure

Non-equilibrium Dynamics of O(N) Nonlinear Sigma models: a Large-N approach

We study the time evolution of the mass gap of the O(N) non-linear sigma model in 2+1 dimensions due to a time-dependent coupling in the large-$N$ limit. Using the Schwinger-Keldysh approach, we derive a set of equations at large $N$ which determine the time dependent gap in terms of the coupling. These equations lead to a criterion for the breakdown of adiabaticity for slow variation of the coupling leading to a Kibble-Zurek scaling law. We describe a self-consistent numerical procedure to solve these large-$N$ equations and provide explicit numerical solutions for a coupling which starts deep in the gapped phase at early times and approaches the zero temperature equilibrium critical point $g_c$ in a linear fashion. We demonstrate that for such a protocol there is a value of the coupling $g= g_c^{\rm dyn}> g_c$ where the gap function vanishes, possibly indicating a dynamical instability. We study the dependence of $g_c^{\rm dyn}$ on both the rate of change of the coupling and the initial temperature. We also verify, by studying the evolution of the mass gap subsequent to a sudden change in $g$, that the model does not display thermalization within a finite time interval $t_0$ and discuss the implications of this observation for its conjectured gravitational dual as a higher spin theory in $AdS_4$.Comment: 22 pages, 9 figures. Typos corrected, references rearranged and added.v3 : sections rearranged, abstract modified, comment about Kibble-Zurek scaling correcte

Variational ansatz for the nonlinear Landau-Zener problem for cold atom association

We present a rigorous analysis of the Landau-Zener linear-in-time term crossing problem for quadratic-nonlinear systems relevant to the coherent association of ultracold atoms in degenerate quantum gases. Our treatment is based on an exact third-order nonlinear differential equation for the molecular state probability. Applying a variational two-term ansatz, we construct a simple approximation that accurately describes the whole-time dynamics of coupled atom-molecular system for any set of involved parameters. Ensuring an absolute error less than for the final transition probability, the resultant solution improves by several orders of magnitude the accuracy of the previous approximations by A. Ishkhanyan et al. developed separately for the weak coupling [J. Phys. A 38, 3505 (2005)] and strong interaction [J. Phys. A 39, 14887 (2006)] limits. In addition, the constructed approximation covers the whole moderate-coupling regime, providing for this intermediate regime the same accuracy as for the two mentioned limits. The obtained results reveal the remarkable observation that for the strong-coupling limit the resonance crossing is mostly governed by the nonlinearity, while the coherent atom-molecular oscillations arising soon after the resonance has been crossed are basically of linear nature. This observation is supposed to be of a general character due to the basic attributes of the resonance crossing processes in the nonlinear quantum systems of the discussed type of involved quadratic nonlinearity

Quasi-spin Model for Macroscopic Quantum Tunnelling between Two Coupled Bose-Einstein Condensates

The macroscopic quantum tunneling between two coupled Bose-Einstein condensates (BEC) (radio-frequency coupled two-component BECs or two BECs confined in a double-well potential) is mapped onto the tunneling of an uniaxial spin with an applied magnetic field. The tunneling exponent is calculated with an imaginary-time path-integral method. In the limit of low barrier, the dependence of tunneling exponent on the system parameters is obtained, and the crossover temperature from thermal regime to quantum regime is estimated. The detailed information about the tunnelling will give help to control population conversion between coupled BECs and realize quantum computation with coupled BECs.Comment: 20 pages, 4 figures, accepted by Phys.Rev.

Unconventional particle-hole mixing in the systems with strong superconducting fluctuations

Development of the STM and ARPES spectroscopies enabled to reach the resolution level sufficient for detecting the particle-hole entanglement in superconducting materials. On a quantitative level one can characterize such entanglement in terms of the, so called, Bogoliubov angle which determines to what extent the particles and holes constitute the spatially or momentum resolved excitation spectra. In classical superconductors, where the phase transition is related to formation of the Cooper pairs almost simultaneously accompanied by onset of their long-range phase coherence, the Bogoliubov angle is slanted all the way up to the critical temperature Tc. In the high temperature superconductors and in superfluid ultracold fermion atoms near the Feshbach resonance the situation is different because of the preformed pairs which exist above Tc albeit loosing coherence due to the strong quantum fluctuations. We discuss a generic temperature dependence of the Bogoliubov angle in such pseudogap state indicating a novel, non-BCS behavior. For quantitative analysis we use a two-component model describing the pairs coexisting with single fermions and study their mutual feedback effects by the selfconsistent procedure originating from the renormalization group approach.Comment: 4 pages, 4 figure