Bogoliubov Approximation Research Articles

Mixture of two unequally charged superfluids in a magnetic field

The artificial magnetic fields engineered for ultracold gases depend on the internal structure of the neutral atoms. Therefore the components of a mixture composed of two atomic gases can exhibit a different response to an artificial magnetic field. Such a mixture can be interpreted as a mixture of two atomic gases, carrying different synthetic charges. We consider such mixtures of two superfluids with unequal synthetic charges in a ring trap subject to a uniform artificial magnetic field. The charge imbalance in such a mixture changes the distribution of excited particles over angular momentum states compared to that of an equally charged mixture. This microscopic difference exhibits macroscopic consequences, such as the occurrence of an angular momentum transfer between two unequally charged components. Due to the interfluid atomic interactions in a ring, the angular momentum transfer can create a counterflowing persistent current in the weakly charged superfluid. Even in the limiting case of a charged and an uncharged superfluid mixture, a persistent current can be induced in the uncharged superfluid, despite the fact that it is not directly coupled to the magnetic field. The stability analysis shows that the induction depends on the interplay between the interfluid interaction and the applied magnetic field. We obtain instability boundaries of the system and construct phase diagrams as a function of the interfluid interaction and the magnetic field. We investigate these properties employing the Bogoliubov approximation.

Low-dimensional self-bound quantum Rabi-coupled bosonic droplets

We analytically calculate the leading quantum corrections of the ground-state energy of two- and one-dimensional weakly interacting Rabi-coupled Bose-Bose mixtures in the frame of the Bogoliubov approximation. We show that to repulsive intraspecies and attractive interspecies interactions, the effect of quantum fluctuations favors the formation of self-bound droplets. These liquidlike states are crucially affected by the Rabi coupling, leading thus to the appearance of a quantum instability. We derive meaningful formulas to describe the droplet phase in the one-dimensional case.

Norm approximation for many-body quantum dynamics: Focusing case in low dimensions

We study the norm approximation to the Schrödinger dynamics of N bosons in Rd (d=1,2) with an interaction potential of the form Ndβ−1w(Nβ(x−y)). Here we are interested in the focusing case w≤0. Assuming that there is complete Bose-Einstein condensation in the initial state, we show that in the large N limit, the evolution of the condensate is effectively described by a nonlinear Schrödinger equation and the evolution of the fluctuations around the condensate is governed by a quadratic Hamiltonian, resulting from Bogoliubov approximation. Our result holds true for all β>0 when d=1 and for all 0<β<1 when d=2.

Breaking of Goldstone modes in a two-component Bose-Einstein condensate

We study the decay rate $\Gamma(k)$ of density excitations of two-component Bose-Einstein condensates at zero temperature. Those excitations, where the two components oscillate in phase, include the Goldstone mode resulting from condensation. While within Bogoliubov approximation the density sector and the spin (out-of-phase) sector are independent, they couple at the three-phonon level. For a Bose-Bose mixture we find that the Belyaev decay is slightly modified due to the coupling with the gapless spin mode. At the phase separation point the decay rate changes instead from the standard $k^5$ to a $k^{5/2}$ behaviour due to the parabolic nature of the spin mode. In presence of coherent coupling between the two components the spin sector is gapped and, away from the ferromagnetic-like phase transition point, the decay of density mode is not affected. On the other hand at the transition point, when the spin fluctuations become critical, the Goldstone mode is not well defined anymore since $\Gamma(k)\propto k$. As a consequence, we show that the friction induced by a moving impurity is enahnced -- a feature which could be experimentally tested. Our results apply to every non-linear 2-component quantum hydrodynamic Hamiltonian which is time-reversal invariant, and possesses an $U(1)\times {\mathbf Z}_2$ symmetry.

A study of shell structure in normal to exotic nuclides within relativistic Hartree–Bogoliubov approximation

The purpose of this work is to study theoretically the shell structure of even–even isotopes in Si, S, Ar and Ca and isotones at neutron number N = 0, 28, 50 and 82. We employed Covariant Relativistic self-consistent mean field models analogous to Kohn–Sham density functional theory to construct the Nuclear Density Functionals from Lagrangian densities based on meson exchange and point coupling models. The pairing correlations of nucleons are considered by the relativistic Hartree–Bogoliubov functional based on quasi-particle operators of Bogoliubov transformations. The theoretical calculations of shell closure parameter [Formula: see text](N) and the differential variation of the two-neutron separation energy [Formula: see text](Z, N) provide recognizable signature of shell closure at N = 14 and 20 in case of Si, N = 14, 20 and 28 in S, Ar and Ca isotopes and are consistent with recent experimental investigations of new sub-shell gaps.

Quantum Theory of Fields and Properties of Quantum Systems

Quantum theory of fields is the most general theory to date. It has an extremely wide field of application: - the physics of elementary particles and their interactions (summarized by the Standard Model); - the physics of the universe close to the Big Bang (primordial fluctuations from which the formation of the structure of the universe originates, evaporation of black holes, Hawking radiation); - the formalism of condensed matter physics, with applications such as superconductivity, superfluidity, phase transitions. Indeed, the quantum theory of fields has been successfully implemented in quantum systems, notably in research on fundamental state energy, elementary excitations spectrum, degeneracy parameters: long range order, Bogoliubov approximation, density matrix diagonalization,…, as well as the characteristics of these systems: movement equation, dynamics of the system,…. Three different quantum systems were concerned in this theoretical study: - a gas of identical atoms of spin zero confined into the trap; - electron gas of spin ½ into the metal; - and a gathering of identical ions of spin zero at high density confined into a radiofrequency linear Paul trap. The microscopic theory was used in the each case and the results obtained by the researchers are presented.

Ground-state properties of interacting Bose polarons

We theoretically investigate the role of multiple impurity atoms on the ground state properties of Bose polarons. The Bogoliubov approximation is applied for the description of the condensate resulting in a Hamiltonian containing terms beyond the Fr\"ohlich approximation. The many-body nature of the impurity atoms is taken into account by extending the many-body description for multiple Fr\"ohlich polarons, revealing the static structure factor of the impurities as the key quantity. Within this formalism various experimentally accessible polaronic properties are calculated such as the energy and the effective mass. These results are examined for system parameters corresponding to two recent experimental realizations of the Bose polaron, one with fermionic impurities and one with bosonic impurities.

Characterization of stimulated excitations in a driven Bose-Einstein condensate

We apply the time-dependent Hartree-Fock-Bogoliubov (td-HFB) theory to describe the stimulated excitation driven by periodically modulating the interactions in a Bose-Einstein condensate (BEC). A comparison with the results calculated from the typical Bogoliubov approximation indicates that the additional interaction terms contributed by the excited modes play an important role to explain the dynamics of the stimulating process. The td-HFB model has not only painted a clear picture of the density wave propagation, but also partly explained the generation of the second order harmonic of the excited modes. The theoretical framework can be directly employed to study similar driven processes.

Roton in a few-body dipolar system

We solve numerically exactly the many-body 1D model of bosons interacting via short-range and dipolar forces and moving in the box with periodic boundary conditions. We show that the lowest energy states with fixed total momentum can be smoothly transformed from the typical states of collective character to states resembling single particle excitations. In particular, we identify the celebrated roton state. The smooth transition is realized by simultaneous tuning short-range interactions and adjusting a trap geometry. With our methods we study the weakly interacting regime as well as the regime beyond the range of validity of the Bogoliubov approximation.

When are two fermions a simple boson? New Gross–Pitaevskii actions for cold Fermi condensates

The BEC regime of a cold fermi gas is characterised by coupled atoms (dimers) which, superficially, look like elementary bosons. We examine how simply-bosonic they really are; firstly, in the Bogoliubov approximation and further, through new actions for the BEC regime in which dimers are represented by coupled Gross–Pitaevskii fields. We find identity at the level of the Bogoliubov approximation in the deep BEC regime, permitting a simple Gross–Pitaevskii description. This fails rapidly as we move towards the BCS regime. However, even in the deep BEC regime there is an intrinsic difference if we go beyond the Bogoliubov approximation. To exemplify this we construct vortex solutions.

Spontaneous Emission Originating from Atomic BEC Interacting with a Single-Mode Quantized Field

In this paper we present a general theoretical model for the interaction between a number of two-level atoms constituting Bose-Einstein condensate (BEC) and a single-mode quantized field. In addition to the usual interacting terms, we take into account interatom as well as higher-order atom-field interactions. To simplify the Hamiltonian of system, after using the Bogoliubov approximation we proceed to calculate the transformed operators of atoms and field. Then, to quantify the spontaneous emission, we get analytical expressions for the expectation value of as the atomic population inversion (API), in the cases of number and coherent states for the atomic subsystem. Our results show that the above-mentioned model interaction leads to the appearance of collapse-revival phenomenon in API. In more detail, the revival time may be tuned by adjusting the interatom interaction constant. Also, the damping process lowers the amplitude of API, but does not change the CR times for weak damping. Moreover, increasing the damping may decrease the number of CRs in a given interval of time such that no revival occurs. Briefly, it may be concluded that in the resonant case the revival times are insensitive to the change of the higher-order atom-field interaction constant and are affected only by the interatom interactions. Finally, we express that, how we can find a practical procedure to measure the quantum states of atoms in BEC.

Anomalous Statistics of Bose-Einstein Condensate in an Interacting Gas: An Effect of the Trap's Form and Boundary Conditions in the Thermodynamic Limit.

We analytically calculate the statistics of Bose-Einstein condensate (BEC) fluctuations in an interacting gas trapped in a three-dimensional cubic or rectangular box with the Dirichlet, fused or periodic boundary conditions within the mean-field Bogoliubov and Thomas-Fermi approximations. We study a mesoscopic system of a finite number of trapped particles and its thermodynamic limit. We find that the BEC fluctuations, first, are anomalously large and non-Gaussian and, second, depend on the trap’s form and boundary conditions. Remarkably, these effects persist with increasing interparticle interaction and even in the thermodynamic limit—only the mean BEC occupation, not BEC fluctuations, becomes independent on the trap’s form and boundary conditions.

Calculation of the critical temperature of a dilute Bose gas in the Bogoliubov approximation

Following an earlier calculation in 3D, we calculate the 2D critical temperature of a dilute, translation-invariant Bose gas using a variational formulation of the Bogoliubov approximation introduced by Critchley and Solomon in 1976. This provides the first analytical calculation of the Kosterlitz-Thouless transition temperature that includes the constant in the logarithm.

Dipolar Bose gas with three-body interactions at finite temperature

We investigate effects of three-body contact interactions on a trapped dipolar Bose gas at finite temperature using the Hartree–Fock–Bogoliubov approximation. We analyze numerically the behavior of the transition temperature and the condensed fraction. Effects of the three-body interactions, anomalous pair correlations and temperature on the collective modes are discussed.

Two-species boson mixture on a ring: A group-theoretic approach to the quantum dynamics of low-energy excitations

We investigate the weak excitations of a system made up of two condensates trapped in a Bose-Hubbard ring and coupled by an interspecies repulsive interaction. Our approach, based on the Bogoliubov approximation scheme, shows that one can reduce the problem Hamiltonian to the sum of sub-Hamiltonians ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{H}}_{k}$, each one associated to momentum modes $\ifmmode\pm\else\textpm\fi{}k$. Each ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{H}}_{k}$ is then recognized to be an element of a dynamical algebra. This uncommon and remarkable property allows us to present a straightforward diagonalization scheme, to find constants of motion, to highlight the significant microscopic processes, and to compute their time evolution. The proposed solution scheme is applied to a simple but nontrivial closed circuit, the trimer. The dynamics of low-energy excitations, corresponding to weakly populated vortices, is investigated considering different choices of the initial conditions and the angular-momentum transfer between the two condensates is evidenced. Finally, the condition for which the spectral collapse and dynamical instability are observed is derived analytically.

Spontaneous Beliaev-Landau scattering out of equilibrium

We investigate Beliaev-Landau scattering in a gas of interacting photons in a coherently driven array of nonlinear dissipative resonators, as described by the 1D driven-dissipative Bose-Hubbard model. Due to the absence of detailed balance in such an out-of-equilibrium setup, steady-state properties can be much more sensitive to the underlying microscopic dynamics. As the popular truncated Wigner approximation dramatically fails in capturing this physics, we present an alternative approach, based on a systematic expansion beyond the Bogoliubov approximation, which includes the third-order correlation functions in the dynamics. As experimentally accessible signatures of Beliaev-Landau processes, we report a small but nonnegligible correction to the Bogoliubov prediction for the steady-state momentum distribution showing a characteristic series of peaks and dips, as well as non-Gaussian features in the statistics of the cavity output field.

Excitations and stability of weakly interacting Bose gases with multibody interactions

We consider weakly interacting bosonic gases with local and non-local multi-body interactions. By using the Bogoliubov approximation, we first investigate contact interactions, studying the case in which the interparticle potential can be written as a sum of N-body {\delta}-interactions, and then considering general contact potentials. Results for the quasi-particle spectrum and the stability are presented. We then examine non-local interactions, focusing on two different cases of 3-body non-local interactions. Our results are used for systems with 2- and 3-body {\delta}-interactions and applied for realistic values of the trap parameters. Finally, the effect of conservative 3-body terms in dipolar systems and soft-core potentials (that can be simulated with Rydberg dressed atoms) is also studied.

Photoneutron cross-section measurements in the Bi209 ( γ,xn ) reaction with a new method of direct neutron-multiplicity sorting

Photoneutron cross sections were measured in the $^{209}\mathrm{Bi}$($\ensuremath{\gamma}, xn$) reaction with $x=1--4$ at energies from the neutron threshold to 40 MeV using quasimonochromatic laser Compton-scattering $\ensuremath{\gamma}$-ray beams. A novel technique of direct neutron-multiplicity sorting with a flat-efficiency detector was used. Results are compared with the positron in-flight annihilation data of Livermore and Saclay as well as with bremsstrahlung data. The present neutron yields are consistent with the latest photoactivation measurement with bremsstrahlung. The giant dipole resonance component of the total photoneutron cross section is reasonably reproduced by model calculations of the Hartree-Fock Bogoliubov plus quasiparticle random phase approximation based on the Gogny D1M interaction for both E1 and M1 components. In contrast, the quasideuteron component of the total photoneutron cross section requires a factor of $\ensuremath{\sim}3$ enhancement of the Levinger parameter. Furthermore, a survival of large $(\ensuremath{\gamma},n)$ cross sections above 20 MeV may indicate the surface effect on the two-component particle-hole state density. The threshold behavior of photoneutron emission is discussed in terms of the average neutron kinetic energy.

Controlling steady-state bipartite entanglement and quadrature squeezing in a membrane-in-the-middle optomechanical system with two Bose-Einstein condensates

We study theoretically a driven hybrid optomechanical system with a membrane-in-the-middle configuration containing two identical elongated cigar-shaped Bose-Einstein condensates (BECs) in each side of the membrane. In the weakly interacting regime, the BECs can be considered as single-mode oscillators in the Bogoliubov approximation which are coupled to the optical field through the radiation pressure interaction so that they behave as two quasi-membranes. We show that the degree of squeezing of each BEC and its entanglement with the moving membrane can be controlled by the \textit{s}-wave scattering frequency of the other one. Since the \textit{s}-wave frequency of each BEC depends on the transverse trapping frequency of the atoms which is an experimentally controllable parameter, one can control the entanglement and squeezing of each BEC through the trapping frequency of the other one.

Binding energy of homogeneous Bose gases

We compute the energy needed to add or remove one particle from a homogeneous system of $N$ bosons on a torus. We focus on the mean-field limit when $N$ becomes large and the strength of particle interactions is proportional to $N^{-1}$, which allows us to justify Bogoliubov's approximation.