75 research outputs found
Mechanical back-reaction effect of the dynamical Casimir emission
We consider an optical cavity enclosed by a freely moving mirror attached to
a spring and we study the quantum friction effect exerted by the dynamical
Casimir emission on the mechanical motion of the mirror. Observable signatures
of this simplest example of back-reaction effect are studied in both the
ring-down oscillations of the mirror motion and in its steady-state motion
under a monochromatic force. Analytical expressions are found in simple yet
relevant cases and compared to complete numerical solution of the master
equation. A circuit-QED device allowing for experimental observation of the
effect with state-of-the-art technology is proposed and theoretically
characterized.Comment: 18 pages, 7 figures; comments are welcom
Field Fluctuations in a One-Dimensional Cavity with a Mobile Wall
We consider a scalar field in a one-dimensional cavity with a mobile wall.
The wall is assumed bounded by a harmonic potential and its mechanical degrees
of freedom are treated quantum mechanically. The possible motion of the wall
makes the cavity length variable, and yields a wall-field interaction and an
effective interaction among the modes of the cavity. We consider the ground
state of the coupled system and calculate the average number of virtual
excitations of the cavity modes induced by the wall-field interaction, as well
as the average value of the field energy density. We compare our results with
analogous quantities for a cavity with fixed walls, and show a correction to
the Casimir potential energy between the cavity walls. We also find a change of
the field energy density in the cavity, particularly relevant in the proximity
of the mobile wall, yielding a correction to the Casimir-Polder interaction
with a polarizable body placed inside the cavity. Similarities and differences
of our results with the dynamical Casimir effect are also discussed.Comment: 5 pages, 2 figure
Fractional differential equations solved by using Mellin transform
In this paper, the solution of the multi-order differential equations, by
using Mellin Transform, is proposed. It is shown that the problem related to
the shift of the real part of the argument of the transformed function, arising
when the Mellin integral operates on the fractional derivatives, may be
overcame. Then, the solution may be found for any fractional differential
equation involving multi-order fractional derivatives (or integrals). The
solution is found in the Mellin domain, by solving a linear set of algebraic
equations, whose inverse transform gives the solution of the fractional
differential equation at hands.Comment: 19 pages, 2 figure
Synthetic gauge potentials and analogue gravity in Bose-Einstein condensates
In this thesis multi-component, spinorial cold atomic gases are studied. We investigate
first the new perspectives introduced by nonlinear, that is density dependent,
synthetic gauge fields in atomic Bose-Einstein condensate. Such fields stem from
a collisionally induced detuning in combination with synthetic magnetism arising
from the light-atom coupling. The effective mean field dynamics of the condensate
shows the appearance of an exotic nonlinearity which is proportional to the current
in the system. It introduces a chirality, whose effects on the stability and dynamical
properties of the rotating state of a condensate is investigated. We show that by
properly shaping the profile and the magnitude of the light-matter interaction parameters,
it may happen that the rotating state is energetically favorable compared
to the corresponding non-rotating one. Furthermore, we analyze the effects of the
nonlinear field on the dynamics of a vortex in a condensate. We obtain the equation
of motion for the vortex core, showing the appearance of an extra force which is
explicitly depending on the number of particles that are in the system.
Furthermore, we consider the implications of the same type of density-dependent
fields in the context of analogue gravity. We show that they provide an extra degreeof-
freedom that can be exploited in order to design effective non-trivial spacetimes
experienced by phonons.
In the framework of analogue models of gravity, we finally discuss the perspectives
of two-dimensional systems, and address the problem of the black hole lasing effect
in the spin modes of the system. By developing a Gross-Pitaevskii theory for
the problem, we prove the onset of the lasing instability, and the phenomenon of
mode conversion at the horizons. To this aim we consider both homogeneous and
harmonically trapped condensates
Quantized vortices in interacting gauge theories
We consider a two-dimensional weakly interacting ultracold Bose gas whose
constituents are two-level atoms. We study the effects of a synthetic
density-dependent gauge field that arises from laser-matter coupling in the
adiabatic limit with a laser configuration such that the single-particle
zero-order vector potential corresponds to a constant synthetic magnetic field.
We find a new exotic type of current non-linearity in the Gross-Pitaevskii
equation which affects the dynamics of the order parameter of the condensate.
We investigate the rotational properties of this system, focusing in particular
on the physical conditions that make the nucleation of a quantized vortex in
the system energetically favourable with respect to the non rotating solution.
We point out that two different physical interpretations can be given to this
new non linearity: firstly it can be seen as a local modification of the mean
field coupling constant, whose value depends on the angular momentum of the
condensate. Secondly, it can be interpreted as a density modulated angular
velocity given to the cloud. Looking at the problem from both of these
viewpoints, we analyze the physical conditions that make a single vortex state
energetically favourable. In the Thomas-Fermi limit, we show that the effect of
the new nonlinearity is to induce a rotation to the condensate, where the
transition from non-rotating to rotating states depends on the density of the
cloud.Comment: 6 pages, one figure. General improvement
Vortex dynamics in superfluids governed by an interacting gauge theory
We study the dynamics of a vortex in a quasi two-dimensional Bose gas
consisting of light matter coupled atoms forming two-component pseudo spins.
The gas is subject to a density dependent gauge potential, hence governed by an
interacting gauge theory, which stems from a collisionally induced detuning
between the incident laser frequency and the atomic energy levels. This
provides a back-action between the synthetic gauge potential and the matter
field. A Lagrangian approach is used to derive an expression for the force
acting on a vortex in such a gas. We discuss the similarities between this
force and the one predicted by Iordanskii, Lifshitz and Pitaevskii when
scattering between a superfluid vortex and the thermal component is taken into
account.Comment: 9 pages. Comments are welcom
Black-hole lasing in coherently coupled two-component atomic condensates
We theoretically study the black-hole lasing phenomenon in a flowing
one-dimensional, coherently coupled two component atomic Bose-Einstein
condensate whose constituent atoms interact via a spin-dependent s-wave contact
interaction. We show by a numerical analysis the onset of the dynamical
instability in the spin branch of the excitations, once a finite supersonic
region is created in this branch. We study both a spatially homogeneous
geometry and a harmonically trapped condensate. Experimental advantages of the
two-component configuration are pointed out, with an eye towards studies of
back-reaction phenomena.Comment: General improvements, corrections and references adde
Noise and dissipation on a moving mirror induced by the dynamical Casimir emission
We adopt an open quantum system approach to study the effects of the
back-reaction from a quantum field onto the dynamics of a moving mirror. We
describe the coupling between the mirror and the field by using a microscopic
model from which the dielectric response of the mirror is obtained from first
principles. Using second-order perturbation theory, we derive the master
equation governing the mechanical motion of the mirror. Our analysis reveals
that the mirror experiences coloured noise and non-local dissipation, which
originate from the emission of particle pairs via the dynamical Casimir effect.
We show that the noise and dissipation kernels, that enter in the definition of
the time-dependent coefficients of the master equation, are related by
fluctuation-dissipation relations.Comment: 16 pages, 2 figures. Submitted to Journal of Physics: Photonics, as
part of Emerging Leaders 2023 Collectio
Nonequilibrium dressing in a cavity with a movable reflecting mirror
We consider a movable mirror coupled to a one-dimensional massless scalar
field in a cavity. Both the field and the mirror's mechanical degrees of
freedom are described quantum-mechanically, and they can interact each other
via the radiation pressure operator. We investigate the dynamical evolution of
mirror and field starting from a nonequilibrium initial state, and their local
interaction which brings the system to a stationary configuration for long
times. This allows us to study the time-dependent dressing process of the
movable mirror interacting with the field, and its dynamics leading to a local
equilibrium dressed configuration. Also, in order to explore the effect of the
radiation pressure on both sides of the movable mirror, we generalize the
effective field-mirror Hamiltonian and previous results to the case of two
cavities sharing the same mobile boundary. This leads us to address, in the
appropriate limit, the dynamical dressing problem of a single mobile wall,
bounded by a harmonic potential, in the vacuum space.Comment: 10 pages, 4 figure
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