A mirror in the vacuum is submitted to a radiation pressure exerted by scattered fields. It is known that the resulting mean force is zero for a motionless mirror, but not for a mirror moving with a non-uniform acceleration. We show here that this force results from a motional modification of the field scattering while being associated with the fluctuations of the radiation pressure on a motionless mirror. We consider the case of a scalar field in a two-dimensional spacetime and characterize the scattering upon the mirror by frequency dependent transmissivity and reflectivity functions obeying unitarity, causality and high frequency transparency conditions. We derive causal expressions for dissipation and fluctuations and exhibit their relation for any stationary input. We recover the known damping force at the limit of a perfect mirror in vacuum. Finally, we interpret the force as a mechanical signature of the squeezing effect associated with the mirror's motion.
A mirror in vacuum is coupled to fluctuating quantum fields. As a result, its energy-momentum and mass fluctuate. We compute the correlation spectra of force and mass fluctuations for a mirror at rest in vacuum (of a scalar field in a two-dimensional space-time). The obtained expressions agree with a mass correction equal to a vacuum energy stored by the mirror. We introduce a Lagrangian model which consistently describes a scalar field coupled to a scatterer, with inertial mass being a quantum variable.
The mean force exerted upon a perfect mirror moving in vacuum in a two dimensional spacetime has the same expression as the radiation reaction force computed in classical electron theory. It follows that unacceptable runaway solutions are predicted. We show that this instability problem does not appear when partially transmitting mirrors are studied. The mechanical impedance describing the mirror coupled to vacuum radiation pressure is computed explicitly; recoil is neglected. It is found to be a passive function, so that stability is ensured. This is connected to the fact that no energy can b…
Vacuum fluctuation, which is the intrinsic nature of an electric field can be measured via homodyne detection. Moreover, electric field intensity fluctuation are also related to vacuum fluctuations. Squeezed vacuum and sub-Poisson light can be obtained by controlling the vacuum fluctuation using noble nonlinear interaction. Based on the squeezed vacuum by inserting a mirror on the unused part of the beam splitter was proposed in 1994, we present the mode matching method for the vacuum and light fields. Light intensity fluctuations also can be reduced by inserting a mirror on the unused part of…
Quantum fluctuations of the vacuum are both a surprising and fundamental phenomenon of nature. Understood as virtual photons flitting in and out of existence, they still have a very real impact, \emph{e.g.}, in the Casimir effects and the lifetimes of atoms. Engineering vacuum fluctuations is therefore becoming increasingly important to emerging technologies. Here, we shape vacuum fluctuations using a "mirror", creating regions in space where they are suppressed. As we then effectively move an artificial atom in and out of these regions, measuring the atomic lifetime tells us the strength of t…
A distant mirror leads to a vacuum-induced level shift in a laser-excited atom. This effect has been measured with a single mirror 25 cm away from a single, trapped barium ion. This dispersive action is the counterpart to the mirror's dissipative effect, which has been shown earlier to effect a change in the ion's spontaneous decay [J. Eschner et al., Nature 413, 495-498 (2001)]. The experimental data are well described by 8-level optical Bloch equations which are amended to take into account the presence of the mirror according to the model in [U. Dorner and P. Zoller, Phys. Rev. A 66, 023816…
We examine temperature cooling of optical chaotic light in a quantum dissipation channel with the damping parameter k.The way we do it is by introducing its thermal vacuum state which can expose entangling effect between the system and the reservoir. The temperature cooling formula is derived, which depends on the parameter k, by adjusting k one can control temperature.
Electromagnetic vacuum fluctuations have observable consequences, like the Casimir force between mirrors in vacuum. This force is now measured with good accuracy and agreement with theory when the effect of imperfect reflection of mirrors is properly taken into account. We discuss the simple case of bulk metallic mirrors described by a plasma model and show that simple scaling laws are obtained at the limits of long and short distances. The crossover between the short and long-distance laws is quite similar to the crossover between Van der Waals and Casimir-Polder forces for two atoms in vacuu…
The force experienced by a mirror moving in vacuum vanishes in the case of uniform velocity or uniform acceleration, as a consequence of spatial symmetries of vacuum. These symmetries do not subsist in a thermal field. We give a general expression of the corresponding viscosity coefficient valid at any temperature and for any reflectivity function. We show that the computed motional force also contains a non vanishing inertial term. The associated mass correction goes to zero in the limiting cases of perfect reflection or of zero temperature.
We consider the vacuum fluctuations contribution to the mass of a mirror in an exactly soluble partially reflecting moving mirror model. Partial reflectivity is accounted for by a repulsive delta-type potential localized along the mirror trajectory. The mirror's mass is explicitly found as an integral functional of the mirror's past trajectory.
We consider the coupling of the electromagnetic vacuum field with an oscillating perfectly-reflecting mirror in the nonrelativistic approximation. As a consequence of the frequency modulation associated to the motion of the mirror, low frequency photons are generated. We calculate the photon emission rate by following a nonperturbative approach, in which the coupling between the field sidebands is taken into account. We show that the usual perturbation theory fails to account correctly for the contribution of TM-polarized vacuum fluctuations that propagate along directions nearly parallel to t…
Compared to the quantum noise in the measurement of the translational motion of a suspended mirror using laser light, the quantum noise in the measurement of the angular motion of a suspended mirror has not been investigated intensively despite its potential importance. In this article, an expression for the quantum noise in the angular motion measurement is explicitly derived. The expression indicates that one quadrature of the vacuum field of the first-order Hermite-Gaussian mode of light causes quantum sensing noise and the other causes quantum backaction noise, or in other words the first-…
We study the accelerated motion of mirrors and the photonic Unruh effect. The solutions of Maxwell's equations with appropriate boundary conditions in Rindler coordinates are found. The canonical quantization of the field is carried out properly. Important consequences arise from the presence of mirrors or polarizers. It is shown that a single reflective surface produces frequency quantization due to Dirichlet conditions applied to the $-1/(αx)^2$ anomalous potential for non-inertial observers. The number of photons per accelerated mode is estimated via Hankel functions.
Observers following special classes of finite-lifetime trajectories have been shown to experience an effective temperature, a generalisation of the Unruh temperature for uniformly accelerated observers. We consider a mirror following such a trajectory - and is hence localised to a strictly bounded causal diamond - that perfectly reflects incoming field modes. We find that inertial observers in the Minkowski vacuum detect particles along the half null-rays at the beginning and end of the mirror's lifetime. These particle distributions exhibit multi-partite entanglement, which reveals novel stru…
Moving mirrors are submitted to reaction forces by vacuum fields. The motional force is known to vanish for a single mirror uniformly accelerating in vacuum. We show that inertial forces (proportional to accelerations) arise in the presence of a second scatterer, exhibiting properties expected for a relative inertia: the mass corrections depend upon the distance between the mirrors, and each mirror experiences a force proportional to the acceleration of the other one. When the two mirrors move with the same acceleration, the mass correction obtained for the cavity represents the contribution t…
The time evolution of thermal states of a mirror released from a tight harmonic trap is studied. After the release no dissipation is assumed to be present and the mirror is, after a time delay, kicked into a momentum superposition state. The thermal character of the initial state washes out the telltale interference patterns of the superposition but no loss of coherence is found. This investigation resolves a controversy about decoherence--without--dissipation and shows that entrained measurements can be surprisingly insensitive to temperature effects.
Two close parallel mirrors attract due to a small force (Casimir effect) originating from the electromagnetic quantum vacuum uctuations of the electromagnetic field. These vacuum uctuations can also induce motional forces exerted upon one mirror when the other one moves. Here we consider an optomechanical system consisting of two vibrating mirrors coupled to an optical resonator. We find that motional forces can determine noticeable coupling rates between the two spatially separated vibrating mirrors. We show that, by tuning the two mechanical oscillators into resonance, energy is exchanged be…
We employ the Schwinger-Keldysh formalism to study the nonequilibrium dynamics of the mirror with perfect reflection moving in a quantum field. Within the regime of linear response in terms of a first order expansion of the mirror's displacement, the coarse-grained effective action is obtained by integrating out quantum fields with the method of influence functional. The semiclassical Langevin equation is derived, and is found to involve two levels of backreaction effects on the dynamics of mirrors: radiation reaction induced by the motion of the mirror and backreaction dissipation arising fro…
In this paper we discuss and review several aspects of the effect of boundary conditions and structured environments on dispersion and resonance interactions involving atoms or molecules, as well as on vacuum field fluctuations. We first consider the case of a perfect mirror, which is free to move around an equilibrium position and whose mechanical degrees of freedom are treated quantum mechanically. We investigate how the quantum fluctuations of the mirror's position affect vacuum field fluctuations for both a one-dimensional scalar and electromagnetic field, showing that the effect is partic…
The Casimir force can be understood as resulting from the radiation pressure exerted by the vacuum fluctuations reflected by boundaries. We extend this local formulation to the case of partially transmitting boundaries by introducing reflectivity and transmittivity coefficients obeying conditions of unitarity, causality and high frequency transparency. We show that the divergences associated with the infiniteness of the vacuum energy do not appear in this approach. We give explicit expressions for the Casimir force which hold for any frequency dependent scattering and any temperature. The corr…
The vacuum radiation of a massive scalar field is studied by means of a single moving mirror. The field equation with an arbitrary-shaped mirror moving in $(d+1)$ dimensions is given perturbatively in the non-relativistic limit. Explicit results are obtained for a flat mirror moving in $(1+1)$ dimensions and $(3+1)$ dimensions. The vacuum radiation power and vacuum friction force on the mirror are given in $(1+1)$ dimensions. The intrinsic mass of the field is found to suppress the vacuum radiation. In $(3+1)$ dimensions, the modification of the frequency spectra and angular spectra of emitted…
We discuss some implications of a very recently obtained result for the force on a slab in a planar cavity based on the calculation of the vacuum Lorentz force [C. Raabe and D.-G. Welsch, Phys. Rev. A 71, 013814 (2005)]. We demonstrate that, according to this formula, the total force on the slab consists of a medium-screened Casimir force and, in addition to it, a medium-assisted force. The sign of of the medium-assisted force is determined solely by the properties of the cavity mirrors. In the Lifshitz configuration, this force is proportional to 1/d at small distances and is very small compa…
We study the resonance interaction between two entangled identical atoms coupled to a quantized scalar field vacuum, and accelerating between two mirrors. We show how radiative processes of the two-atom entangled state can be manipulated by the atomic configuration undergoing noninertial motion. Incorporating the Heisenberg picture with symmetric operator ordering, the vacuum fluctuation and the self-reaction contributions are distinguished. We evaluate the resonance energy shift and the relaxation rate of energy of the two atom system from the self-reaction contribution in the Heisenberg equa…
In this paper, we theoretically investigate the displacement and momentum fluctuations spectra of the movable mirror in a standard optomechanical system driven by a finite bandwidth squeezed vacuum light accompanying a coherent laser field. Two cases in which the squeezed vacuum is generated by degenerated and non-degenerate parametric oscillators (DPO and NDPO) are considered. We find that for the case of finite bandwidth squeezed vacuum injection, the two spectra exhibit unique features, which strongly differ from those of broadband squeezing excitation. In particular, the spectra exhibit a …
Radiation from a mirror moving in vacuum electromagnetic fields is shown to vanish in the case of a uniformly accelerated motion. Such motions are related to conformal coordinate transformations, which preserve correlation functions characteristic of vacuum fluctuations. As a result, vacuum fluctuations remain invariant under reflection upon a uniformly accelerated mirror, which therefore does not radiate and experiences no radiation reaction force. Mechanical effects of vacuum fluctuations thus exhibit an invariance with respect to uniformly accelerated motions.
The entanglement of the two movable mirrors in a single mode cavity field is studied in an ideal situation without thermal noise. When gn/w <<1 where g is the coupling coefficient between the mirror and the field, w is the mirror' vibration frequency and n is photon number of the cavity field, we work out Wootters concurrence of the system initially with the field in Fock number state and the two mirrors in vacuum states, and find that the states of the mirrors are entangled into space spanned by |0>,|1> via radiation pressure, though the concurrence is very small.
On this work, we consider a particle moving in front of a dielectric plate, and study two of the most relevant effects of the vacuum field fluctuations: the dissipation, and the decoherence of the particle's internal degrees of freedom. We consider the particle to follow a classical, macroscopically-fixed trajectory. To study the dissipative effects, we calculate the in-out effective action by functionally integrating over the vacuum field and the microscopic degrees of freedom of both the plate and the particle. This in-out effective action develops an imaginary part, hence a non-vanishing pr…
We show that an atom can be coupled to a mechanical oscillator via quantum vacuum fluctuations of a cavity field enabling energy transfer processes between them. In a hybrid quantum system consisting of a cavity resonator with a movable mirror and an atom, these processes are dominated by two pair-creation mechanisms: the counterrotating (atom-cavity system) and dynamical Casimir interaction terms (optomechanical system). Because of these two pair-creation mechanisms, the resonant atom-mirror coupling is the result of high-order virtual processes with different transition paths well described …
Vacuum field fluctuations exert a radiation pressure which induces mechanical effects on scatterers. The question naturally arises whether the energy of vacuum fluctuations gives rise to inertia and gravitation in agreement with the general principles of mechanics. As a new approach to this question, we discuss the mechanical effects of quantum field fluctuations on two mirrors building a Fabry-Perot cavity. We first put into evidence that the energy related to Casimir forces is an energy stored on field fluctuations as a result of scattering time delays. We then discuss the forces felt by the…
We consider a simple (1+1)-dimensional model for the Casimir-Polder interaction consisting of two oscillators coupled to a scalar field. We include dissipation in a first principles approach by allowing the oscillators to interact with heat baths. For this system, we derive an expression for the free energy in terms of real frequencies. From this representation, we derive the Matsubara representation for the case with dissipation. Further we consider the case of vanishing intrinsic frequencies of the oscillators. We show that in this case the contribution from the zeroth Matsubara frequency ge…
We calculate the Casimir energy for scalar and gauge fields in interaction with zero-width mirrors, including quantum effects due to the matter fields inside the mirrors. We consider models where those fields are either scalar or fermionic, obtaining general expressions for the energy as a function of the vacuum field 1PI function. We also study, within the frame of a concrete model, the role of the dissipation induced by those degrees of freedom, showing that, after integration of the matter fields, the effective theory for the electromagnetic field contains modes with complex energies. As fo…
We study the dynamics of a general quartic interaction Hamiltonian under the influence of dissipation and non-classical driving. We show that this scenario could be realised with a cascaded superconducting cavity-qubit system in the strong dispersive regime in a setup similar to recent experiments. In the presence of dissipation, we find that an effective Hartree-type decoupling with a Fokker-Planck equation yields a good approximation. We find that the stationary state is approximately a squeezed vacuum, which is enhanced by the $Q$-factor of the cavity but conserved by the interaction. The q…
To observe the dynamical Casimir effect (DCE) induced by a moving mirror is a long-standing challenge because the mirror velocity needs to approach the speed of light. Here, we present an experimentally feasible method for observing this mechanical DCE in an optomechanical system. It employs a detuned, parametric driving to squeeze a cavity mode, so that the mechanical mode, with a typical resonance frequency, can parametrically and resonantly couple to the squeezed cavity mode, thus leading to a resonantly amplified DCE in the squeezed frame. The DCE process can be interpreted as {\it mechani…
We calculated the force of the quantum vacuum, the Casimir force, in a spherically symmetric medium, Maxwell's fish eye, surrounded by a perfect mirror and derived an exact analytic solution. Our solution questions the idea that the Casimir force of a spherical mirror is repulsive - we found an attractive force that diverges at the mirror.
Positive frequency Wightman function and vacuum expectation values of the energy-momentum tensor are computed for a massive scalar field with general curvature coupling parameter and satisfying Robin boundary condition on a uniformly accelerated infinite plate. The both regions of the right Rindler wedge, (i) on the right (RR region) and (ii) on the left (RL region) of the plate are investigated. For the case (ii) the electromagnetic field is considered as well. The mode summation method is used with combination of a variant of the generalized Abel-Plana formula. This allows to present the exp…
We note that massless fields within the future and past light cone may be quantized as independent systems. We show that the vacuum is an entangled state of these systems, exactly mirroring the known entanglement between the spacelike separated Rindler wedges. We describe a detector which exhibits a thermal response to the vacuum when switched on at t=0. The feasibility of experimentally detecting this effect is discussed.
Considering the neutrino state like an open quantum system, we analyze its propagation in vacuum or in matter. After defining what can be called decoherence and relaxation effects, we show that in general the probabilities in vacuum and in constant matter can be written in a similar way, which is not an obvious result in this approach. From this result, we analyze the situation where neutrinos evolution satisfies the adiabatic limit and use this formalim to study solar neutrinos. We show that the decoherence effect may not be bounded by the solar neutrino data and review some results in the li…
Quantum fluctuations impose fundamental limits on measurement and space-time probing. Although using optimised probe fields can allow to push sensitivity in a position measurement beyond the "standard quantum limit", quantum fluctuations of the probe field still result in limitations which are determined by irreducible dissipation mechanisms. Fluctuation-dissipation relations in vacuum characterise the mechanical effects of radiation pressure vacuum fluctuations, which lead to an ultimate quantum noise for positions. For macroscopic reflectors, the quantum noise on positions is dominated by gr…
An excited-state atom whose emitted light is back-reflected by a distant mirror can experience trapping forces, because the presence of the mirror modifies both the electromagnetic vacuum field and the atom's own radiation reaction field. We demonstrate this mechanical action using a single trapped barium ion. We observe the trapping conditions to be notably altered when the distant mirror is shifted by an optical wavelength. The well-localised barium ion enables the spatial dependence of the forces to be measured explicitly. The experiment has implications for quantum information processing a…
We consider a dissipative evolution of parametrically-driven qubits-cavity system under the periodical modulation of coupling energy between two subsystems, which leads to the amplification of counterrotating processes. We reveal a very rich dynamical behavior of this hybrid system. In particular, we find that the energy dissipation in one of the subsystems can enhance quantum effects in another subsystem. For instance, optimal cavity decay assists to stabilize entanglement and quantum correlations between qubits even in the steady state and to compensate finite qubit relaxation. On the contra…
We consider an atom (represented by a two-level system) moving in front of a dielectric plate, and study how traces of dissipation and decoherence (both effects induced by vacuum field fluctuations) can be found in the corrections to the unitary geometric phase accumulated by the atom. We consider the particle to follow a classical, macroscopically-fixed trajectory and integrate over the vacuum field and the microscopic degrees of freedom of both the plate and the particle in order to calculate friction effects. We compute analytically and numerically the non-unitary geometric phase for the mo…
We study the dynamical Casimir effect using a fully quantum-mechanical description of both the cavity field and the oscillating mirror. We do not linearize the dynamics, nor do we adopt any parametric or perturbative approximation. By numerically diagonalizing the full optomechanical Hamiltonian, we show that the resonant generation of photons from the vacuum is determined by a ladder of mirror-field {\em vacuum Rabi splittings}. We find that vacuum emission can originate from the free evolution of an initial pure mechanical excited state, in analogy with the spontaneous emission from excited …
Creation of scalar massless particles in two-dimensional Minkowski space-time--as predicted by the dynamical Casimir effect--is studied for the case of a semitransparent mirror initially at rest, then accelerating for some finite time, along a trajectory that simulates a black hole collapse (defined by Walker, and Carlitz and Willey), and finally moving with constant velocity. When the reflection and transmission coefficients are those in the model proposed by Barton, Calogeracos, and Nicolaevici [$r(w)=-iα/(\w+iα)$ and $s(w)=\w/(\w+iα)$, with $α\geq 0$], the Bogoliubov coefficients on the bac…
In this paper we dwell on three issues: 1) revisit the relation between vacuum fluctuations and radiation reaction in atom-field interactions, which began in the 70s and settled in the 90s with its resolution recorded in monographs; 2) the fluctuation-dissipation relation (FDR) of the system, pointing out the differences between that in linear response theory (LRT) assuming ultra-weak coupling between the system and the bath, and the FDR in an equilibrated final state, relaxed from the nonequilibrium evolution of an open quantum system; 3) quantum radiation from an atom interacting with a quan…
We consider a system consisting of a quantum, massless, real scalar field, in the presence of nonlinear mirrors: infinite parallel planes, upon which the field satisfies nonlinear boundary conditions. The latter are implemented by non-quadratic interaction vertices, strictly localized on the mirrors. By using the appropriate perturbative expansions, we obtain approximate expressions for the Casimir energy corresponding to weak coupling, regarding the strength of the interaction terms. We also comment on an alternative expansion scheme that may be useful when the weak coupling expansion is not …
In this paper at first we successfully teleport the unknown quantum state which is a superposition of squeezed vacuum state and squeezed one-photon state using the beam splitter in the absence of dissipation. In the continuation, we try to implement the same teleportation protocol, however, in the presence of dissipation effects. To do this task, we use proper entangled channel to reach to perfect teleportation under the in uence of decoherence. Finally, we consider another superposition of two squeezed vacuum states with separation in phase and teleport it with a different appropriate entangl…
The partner mode with respect to a vacuum state for a given mode (like that corresponding to one of the thermal particles emitted by a black hole) is defined and calculated. The partner modes are explicitly calculated for a number of cases, in particular for the modes corresponding to a particle detector being excited by turn-on/turn-off transients, or with the thermal particles emitted by the accelerated mirror model for black hole evaporation. One of the key results is that the partner mode in general is just a vacuum fluctuation, and one can have the partner mode be located in a region wher…
We study dissipative effects due to inertial forces acting on matter fields confined to accelerated boundaries in $1+1$, $2+1$, and $3+1$ dimensions. These matter fields describe the internal degrees of freedom of `mirrors' and impose, on the surfaces where they are defined, boundary conditions on a fluctuating `vacuum' field. We construct different models, involving either scalar or Dirac matter fields coupled to a vacuum scalar field, and use effective action techniques to calculate the strength of dissipation. In the case of massless Dirac fields, the results could be used to describe the i…
We study the Casimir interaction energy due to the vacuum fluctuations of the Electromagnetic (EM) field in the presence of two mirrors, described by $2+1$-dimensional, generally nonlocal actions, which may contain both parity-conserving and parity-breaking terms. We compare the results with the ones corresponding to Chern-Simons boundary conditions, and evaluate the interaction energy for several particular situations.
The Brownian motion of small particles interacting with a field at a finite temperature is a well-known and well-understood phenomenon. At zero temperature, even though the thermal fluctuations are absent, quantum fields still possess vacuum fluctuations. It is then interesting to ask whether a small particle that is interacting with a quantum field will exhibit Brownian motion when the quantum field is assumed to be in the vacuum state. In this paper, we study the cases of a small charge and an imperfect mirror interacting with a quantum scalar field in (1+1) dimensions. Treating the quantum …
