A path integral formulation is developed for the dynamic Casimir effect. It allows us to study arbitrary deformations in space and time of the perfectly reflecting (conducting) boundaries of a cavity. The mechanical response of the intervening vacuum is calculated to linear order in the frequency-wavevector plane. For a single corrugated plate we find a correction to mass at low frequencies, and an effective shear viscosity at high frequencies; both anisotropic. For two plates there is resonant dissipation for all frequencies greater than the lowest optical mode of the cavity.
We consider a model for an oscillatory, relativistic accelerating photodetector inside a cavity and show that the entangled photon pair production from the vacuum (Unruh effect) can be accurately described in the steady state by a non-degenerate parametric amplifier (NDPA), with the detector's accelerating center of mass serving as the parametric drive (pump). We propose an Unruh effect analogue NDPA microwave superconducting circuit scheme, where the breathing mode of the coupling capacitance between the cavity and detector provides the mechanical pump. For realizable circuit parameters, the …
We consider a two-photon Rabi model with one of the cavity mirrors connected by a mechanical oscillator in strong-coupling regime. We find that when the cavity is in its vacuum state, there exists a resonant coupling between the atom and mechanical oscillator even if the quality factor of the cavity is ultra low. The coupling is coherent and can be achieved by the exchange of virtual photon pairs induced by dynamical Casimir effect. Moreover, when considering the one-photon Rabi model, we find that the atom can absorb one photon from a virtual photon pair, leaving the other converting to a rea…
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 …
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 …
Abstract This paper provides elements in support of the random zero-point radiation field (zpf) as an essential ontological ingredient needed to explain distinctive properties of quantum-mechanical systems. We show that when an otherwise classical particle is connected to the zpf, a drastic, qualitative change in the dynamics takes place, leading eventually to the quantum dynamics. In particular, we demonstrate that in parallel with the evolution of the particle canonical variables into quantum operators satisfying the basic commutator \left[\hat{x},\hat{p}\right]=i\hbar, also the field canoni…
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…
The strength of optomechanical interactions in a cavity optomechanical system can be quantified by a vacuum coupling rate $\vcr$ analogous to cavity quantum electrodynamics. This single figure of merit removes the ambiguity in the frequently quoted coupling parameter defining the frequency shift for a given mechanical displacement, and the effective mass of the mechanical mode. Here we demonstrate and verify a straightforward experimental technique to derive the vacuum optomechanical coupling rate. It only requires applying a known frequency modulation of the employed electromagnetic probe fie…
The quantum field of a single particle is expressed as the sum of the particle's ordinary wave function and the vacuum fluctuations. An exact quantum-field calculation shows that the squared amplitude of this field sums, at any time, to a delta function representing a discrete corpuscle at one point and zero everywhere else. The peak of the delta function is located at the point where the vacuum fluctuations interfere constructively with the ordinary wave function. Similarly, the collapsed wave function after a measurement of an observable is determined by interference between the initial wave…
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 investigate theoretically a hybrid system consisting of a Bose-Einstein condensate (BEC) trapped inside a laser driven membrane-in-the-middle optomechanical cavity assisted with squeezed vacuum injection whose moving membrane interacts both linearly and quadratically with the radiation pressure of the cavity. It is shown that such a hybrid system is very suitable for generating strong quadrature squeezing in the mechanical mode of the membrane and the Bogoliubov mode of the BEC in the unresolved sideband regime. More interestingly, by choosing a suitable sign for the quadratic optomechanica…
We investigate the dynamics of a two-level atom flying through a photonic cavity when the light-matter interaction is in the ultrastrong coupling regime. We adopt a closed full quantum description that takes into account the quantization of the atom center-of-mass motion in addition to its internal degree of freedom and to the quantized photonic cavity field. We find that multiple qualitatively different dynamical regimes are achievable according to two key figures of merit: the ratio between the kinetic energy and the bare excitation energies, and the product of these bare energies with the t…
We show that the interpretation of $\mathbf{D}=\varepsilon_{0} \mathbf{E}$ as vacuum polarization is consistent with quantum electrodynamics. A free electromagnetic field polarizes the vacuum but the magnetization and polarization currents cancel giving zero source current. The speed of light is a universal constant while the fine structure constant that couples the EM field to matter runs. In that sense, the quantum vacuum can be understood as a modern Lorentz invariant ether.
Position measurements at the quantum level are vital for many applications, but also challenging. Typically, methods based on optical phase shifts are used, but these methods are often weak and difficult to apply to many materials. An important example is graphene, which is an excellent mechanical resonator due to its small mass and an outstanding platform for nanotechnologies, but is largely transparent. Here, we present a novel detection scheme based upon the strong, dispersive vacuum interactions between a graphene sheet and a quantum emitter. In particular, the mechanical displacement caus…
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 …
Ben-Israel and Vaidman (Found Phys (2017). doi:10.1007/s10701-017-0071-x) have raised objections to my arguments that there are cases where a quantum mechanical weak value can be said not to represent the system to which it pertains. They are correct in pointing out that some of my conclusions were too general. However, for weak values of projection operators my conclusions still stand.
Sympathetic laser cooling of a single mode graphene membrane coupled to an atomic cloud interacting via Casimir-Polder forces has been recently proposed. Here, we extend this study to the effect of secondary graphene membrane whose frequency may be far or close to resonance. We show that if the two mechanical modes are close together, it is possible to simultaneously cool both modes. Conversely, if the two frequencies are set far apart, the secondary mode does not affect the cooling of the first one. We also study the entanglement properties of the steady-state using the logarithmic negativity…
The quantum transition between shifted zero-mode wave functions is shown to be induced by the systematic deformation of topological and non-topological defects that support the $1$-dim double-well (DW) potential tunneling dynamics. The topological profile of the zero-mode ground state, $ψ_{0}$, and the first excited state, $ψ_{1}$, of DW potentials is obtained through the analytical technique of topological defect deformation. Deformed defects create two inequivalent topological scenarios connected by a symmetry breaking that support the quantum conversion of a zero-mode stable vacuum into an …
We describe vacuum fluctuations and photon-field correlations in interacting quantum mechanical light-matter systems, by generalizing the application of mixed quantum-classical dynamics techniques. We employ the multi-trajectory implementation of Ehrenfest mean field theory, traditionally developed for electron-nuclear problems, to simulate the spontaneous emission of radiation in a model quantum electrodynamical cavity-bound atomic system. We investigate the performance of this approach in capturing the dynamics of spontaneous emission from the perspective of both the atomic system and the ca…
We propose and analyse a feasible experimental scheme for a quantum force sensor based on the elimination of back-action noise through coherent quantum noise cancellation (CQNC) in a hybrid atom-cavity optomechanical setup assisted with squeezed vacuum injection. The force detector, which allows for a continuous, broad-band detection of weak forces well below the standard quantum limit (SQL), is formed by a single optical cavity simultaneously coupled to a mechanical oscillator and to an ensemble of ultracold atoms. The latter acts as a negative-mass oscillator so that atomic noise cancels exa…
We explore theoretically the optical response properties in an optomechanical system under electromagneti- cally induced transparency condition but with the mechanical resonator being driven by an additional coherent field. In this configuration, more complex quantum coherent and interference phenomena occur. In partic- ular, we find that the probe transmission spectra depend on the total phase of the applied fields. Our study also provides an efficient way to control propagation of amplification.
When one tries to take into account the non-trivial vacuum structure of Quantum Field Theory, the standard functional-integral tools such as generating functionals or transitional amplitudes, are often quite inadequate for such purposes. Here we propose a generalized generating functional for Green's functions which allows to easily distinguish among a continuous set of vacua that are mutually connected via unitary canonical transformations. In order to keep our discussion as simple as possible, we limit ourselves to Quantum Mechanics where the generating functional of Green's functions is con…
In the existing expositions of the Karolyhazy model, quantum mechanical uncertainties are mimicked by classical spreads. It is shown how to express those uncertainties through entities of the future unified theory of general relativity and quantum theory.
In the context of inflation, non-vacuum initial states for cosmological perturbations that possess a built in scale are studied. It is demonstrated that this assumption leads to a falsifiable class of models. The question of whether they lead to conflicts with the available observations is addressed. For this purpose, the power spectrum of the Bardeen potential operator is calculated and compared with the CMBR anisotropies measurements and the redshift surveys of galaxies and clusters of galaxies. Generic predictions of the model are: a high first acoustic peak, the presence of a bump in the m…
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 investigate theoretically in detail the non-linear effects in the response of an optical/microwave cavity coupled to a Duffing mechanical resonator. The cavity is driven by a laser at a red or blue mechanical subband, and a probe laser measures the reflection close to the cavity resonance. Under these conditions, we find that the cavity exhibits optomechanically induced reflection (OMIR) or absorption (OMIA) and investigate the optomechanical response in the limit of non-linear driving of the mechanics. Similar to linear mechanical drive, an overcoupled cavity the red-sideband drive may lea…
We determine the small signal gain and noise response of an amplifier based on the nonlinear response of a quantum nanomechanical resonator. The resonator is biased in the nonlinear regime by a strong harmonic bias force and we determine the response to a small additional driving signal detuned with respect to the bias force.
This approach to the incorporation of stochastic thermodynamics into quantum theory is based on the conception of consistent inclusion of the holistic stochastic environmental influence described by wave functions of the arbitrary vacuum, which was proposed in our paper previously. In this study, we implement the possibility of explicitly incorporating the zeroth law of stochastic thermodynamics in the form of the saturated Schrödinger uncertainty relation into quantum theory. This allows comparatively analyzing the sets of states of arbitrary vacuums, namely, squeezed coherent states (SCSs) a…
We consider a standard optomechanical system where a mechanical oscillator is coupled to a cavity mode through the radiation pressure interaction. The oscillator is coherently driven at its resonance frequency, whereas the cavity mode is driven below its resonance, providing optical damping of the mechanical oscillations. We study the nonlinear coherent response of the mechanical oscillator in this setup. For large mechanical amplitudes, we find that the system can display dynamical multistability if the optomechanical cooperativity exceeds a critical value. This analysis relates standard opto…
We investigate the optical response of a hybrid electro-optomechanical system interacting with a qubit. In our experimentally feasible system, tunable all-optical-switching, double-optomechanically induced transparency (OMIT) and optomechanically induced absorption (OMIA) can be realized. The proposed system is also shown to generate anomalous dispersion. Based on our theoretical results, we provide a tunable switch between OMIT and OMIA of the probe field by manipulating the relevant system parameters. Also, the normal-mode-splitting (NMS) effect induced by the interactions between the subsys…
Nonlinearity in macroscopic mechanical system plays a crucial role in a wide variety of applications, including signal transduction and processing, synchronization, and building logical devices. However, it is difficult to generate nonlinearity due to the fact that macroscopic mechanical systems follow the Hooke's law and response linearly to external force, unless strong drive is used. Here we propose and experimentally realize a record-high nonlinear response in macroscopic mechanical system by exploring the anharmonicity in deforming a single chemical bond. We then demonstrate the tunabilit…
We theoretically investigate the analog of electromagnetically induced transparency, absorption and parametric amplification in a hybrid opto-electromechanical system consisting of an optical cavity and a microwave cavity coupled to a common nanomechanical resonator. When the two cavity modes are driven on their respective red sidebands by two pump beams and a probe beam is applied to the optical cavity to monitor the optical response of the hybrid system, we find that a transparency window appears in the probe transmission spectrum due to destructive interference. When the optical cavity is p…
The analysis of uniformly longitudinally extended detector is performed and it is shown that the response of such a detector does not differ from the response of the Unruh detector, but the its excitation is caused not by the thermal bath, but by interaction with the fluctuations of the quantum field by virtual quanta.
