Bogoliubov Vacuum Research Articles

Effective mesonic theory for the ’t Hooft model on the lattice

We apply to a lattice version of the ’t Hooft model, QCD in two space–time dimensions for large number of colours, a method recently proposed to obtain an effective mesonic action starting from the fundamental, fermionic one. The idea is to pass from a canonical, operatorial representation, where the low-energy states have a direct physical interpretation in terms of a Bogoliubov vacuum and its corresponding quasiparticle excitations, to a functional, path integral representation, via the formalism of the transfer matrix. In this way we obtain a lattice effective theory for mesons in a self-consistent setting. We also verify that well-known results from other different approaches are reproduced in the continuum limit.

Recursive Construction of the Bosonic Bogoliubov Vacuum State

In this work we derive a novel procedure for obtaining the bosonic Bogoliubov vacuum states by using a recursive scheme. The vacuum state for the new creation and annihilation operators is explicitly constructed in terms of the number states of the old operators, which are connected by a Bogoliubov transformation. The coefficients of the ground state in Fock basis are thus obtained as exclusive functions of the parameters of the Bogoliubov transformations.

Macrostates Thermodynamics and Its Stable Classical Limit in Global One-Dimensional Quantum General Relativity

Global One Dimensional Quantum General Relativity is the toy model with nontrivial eld theoretical content, describing classical one-dimensional massive bosonic elds related to any 3 + 1 metric, where the dimension is a volume of threedimensional embedding. In fact it constitutes the midisuperspatial Quantum Gravity model. We use one-particle density operator method in order to building macrostates thermodynamics related with any 3 + 1 metric. Taking the Boltzmann gas limit, which is given by the energy equipartition law for the Bose Einstein gas of space quantum states generated from the Bogoliubov vacuum, we receive consistent with General Relativity thermodynamical degrees of freedom number. Concepts of Physics, Vol. VI, No. 1(2009) DOI: 10.2478/v10005-009-0002-5 19 It con rm that the proposed Quantum Gravity toy model has well-de ned classical limit in accordance with classical gravity theory. 20 Concepts of Physics, Vol. VI, No. 1 (2009) Macrostates thermodynamics ...

Methods for Detecting Acceleration Radiation in a Bose-Einstein Condensate

We propose and study methods for detecting Unruh-like acceleration radiation effects in a Bose-Einstein condensate in a (1+1)-dimensional setup. The Bogoliubov vacuum of a Bose-Einstein condensate is used to simulate a scalar field theory, and accelerated atom dots or optical lattices serve as detectors of phonon radiation due to acceleration effects. In particular, we study the dispersive effects of the Bogoliubov spectrum on the ideal case of exact thermalization. Our results suggest that acceleration radiation effects can be observed using currently accessible experimental methods.

N-conserving Bogoliubov vacuum of a two-component Bose–Einstein condensate: density fluctuations close to a phase-separation condition

Two-component Bose–Einstein condensates are considered within a number conserving version of the Bogoliubov theory. We show that the Bogoliubov vacuum state can be obtained in the particle representation in a simple form. We predict considerable density fluctuations in finite systems close to the phase-separation regime. We analyze homogeneous condensates and condensates in a double-well potential.

Images of a Bose-Einstein condensate in position and momentum space

In the Bogoliubov theory a condensate initially prepared in its ground state described by stationary Bogoliubov vacuum and later perturbed by a time-dependent potential or interaction strength evolves into a time-dependent excited state which is dynamical Bogoliubov vacuum. The dynamical vacuum has a simple diagonal form in a time-dependent orthonormal basis of single particle modes. This diagonal representation leads to a gaussian probability distribution for possible outcomes of density measurements in position and momentum space. In these notes we also discuss relations with the U(1) symmetry breaking version of the Bogoliubov theory and give two equivalent gaussian integral representations of the dynamical vacuum state.

N-particle Bogoliubov vacuum state

We consider the Bogoliubov vacuum state in the number-conserving Bogoliubov theory proposed by Castin and Dum [Phys. Rev. A 57, 3008 (1998)]. We show that in the particle representation the vacuum can be written in a simple diagonal form. The vacuum state can describe the stationary N-particle ground state of a condensate in a trap, but it can also represent a dynamical state when, for example, a Bose-Einstein condensate initially prepared in the stationary ground state is subject to a time-dependent perturbation. In both cases the diagonal form of the Bogoliubov vacuum can be obtained by basically diagonalizing the reduced single particle density matrix of the vacuum. We compare N-body states obtained within the Bogoliubov theory with the exact ground states in a 3-site Bose-Hubbard model. In this example, the Bogoliubov theory fails to accurately describe the stationary ground state in the limit when N goes to infinity but a small fraction of depleted particles is kept constant.

Hamiltonian cosmological perturbation theory

The Hamiltonian approach to cosmological perturbations in general relativity in finite space–time is developed, where a cosmological scale factor is identified with spatial averaging the metric determinant logarithm. This identification preserves the number of variables and leads to a cosmological perturbation theory with the scalar potential perturbations in contrast to the kinetic perturbations in the Lifshitz version which are responsible for the “primordial power spectrum” of CMB in the inflationary model. The Hamiltonian approach enables to explain this “spectrum” in terms of scale-invariant variables and to consider other topical problem of modern cosmology in the context of quantum cosmological creation of both universes and particles from the stable Bogoliubov vacuum.

Images of a Bose–Einstein condensate: diagonal dynamical Bogoliubov vacuum

Evolution of a Bose–Einstein condensate subject to a time-dependent external perturbation can be described by a time-dependent number-conserving Bogoliubov theory: a condensate initially in its ground state Bogoliubov vacuum evolves into a time-dependent excited state which can be formally written as a time-dependent Bogoliubov vacuum annihilated by time-dependent quasiparticle annihilation operators. We prove that any Bogoliubov vacuum can be brought to a diagonal form in a time-dependent orthonormal basis. This diagonal form is tailored for simulations of quantum measurements on an excited condensate. As an example we work out phase imprinting of a dark soliton followed by a density measurement.

Entanglement in the Bogoliubov vacuum

We analyze the entanglement properties of the Bogoliubov vacuum, which is obtained as a second order approximation to the ground state of an interacting Bose--Einstein condensate. We work on one and two dimensional lattices and study the entanglement between two groups of lattice sites as a function of the geometry of the configuration and the strength of the interactions. As our measure of entanglement we use the logarithmic negativity, supplemented by an algorithmic check for bound entanglement where appropriate. The short-range entanglement is found to grow approximately linearly with the group sizes and to be favored by strong interactions. Conversely, long range entanglement is favored by relatively weak interactions. Working with periodic boundary conditions we find some surprising finite size effects for the very long range entanglement. No examples of bound entanglement is found.

Depletion of the dark soliton: The anomalous mode of the Bogoliubov theory

Quantum depletion from an atomic quasi-one-dimensional Bose-Einstein condensate with a dark soliton is studied in a framework of the Bogoliubov theory. Depletion is dominated by an anomalous mode localized in a notch of the condensate wave function. Depletion in an anomalous mode requires a different treatment than depletion without anomalous modes. In particular, quantum depletion in the Bogoliubov vacuum of the anomalous mode is experimentally irrelevant. A dark soliton is initially prepared in a state with minimal depletion, which is not a stationary state of the Bogoliubov theory. The notch fills up with incoherent atoms depleted from the condensate. For realistic parameters the filling time can be as short as 10 ms.

REPARAMETRIZATION-INVARIANT PATH INTEGRAL IN GR AND "BIG BANG" OF QUANTUM UNIVERSE

The reparametrization-invariant generating functional for the unitary and causal perturbation theory in general relativity in a finite space–time is obtained. The region of validity of the Faddeev–Popov–DeWitt functional is studied. It is shown that the invariant content of general relativity as a constrained system can be covered by two "equivalent" unconstrained systems: the "dynamic" (with "dynamic" evolution parameter as the metric scale factor) and "geometric" (given by the Levi–Civita type canonical transformation to the action-angle variables where the energy constraint converts into a new momentum). "Big Bang," the Hubble evolution, and creation of matter fields by the "geometric" vacuum are described by the inverted Levi–Civita transformation of the geomeric system into the dynamic one. The particular case of the Levi–Civita transformations are the Bogoliubov ones of the particle variables (diagonalizing the dynamic Hamiltonian) to the quasiparticles (diagonalizing the equations of motion). The choice of initial conditions for the "Big Bang" in the form of the Bogoliubov (squeezed) vacuum reproduces all stages of the evolution of the Friedmann–Robertson–Walker universe in their conformal (Hoyle–Narlikar) versions.