We present an open quantum system theory of atom interferometers evolving in the quantized electromagnetic field bounded by an ideal conductor. Our treatment reveals an unprecedented feature of matter-wave propagation, namely the appearance of a non-local double-path phase coherence. In the standard interpretation of interferometers, one associates well-defined separate phases to individual paths. Our non-local phase coherence is instead associated to pairs of paths. It arises from the coarse-graining over the quantized electromagnetic field and internal atomic degrees of freedom, which play the role of a common reservoir for the pair of paths and lead to a non-Hamiltonian evolution of the atomic waves. We develop a diagrammatic interpretation and estimate the non-local phase for realistic experimental parameters.PACS numbers: 03.75.Dg Atom interferometry [1] has become a field of great importance for both basic and applied science, enabling, in particular, the realization of extremely accurate inertial sensors [2,3]. With the advent of the coherent atomic waves guided on chips [4], the investigation of atom-surface interactions has become a frontier for such systems. Already, atom interferometers have been used to probe the van der Waals regime [5]. This experimental effort calls for a complete theory of atom interferometers in the presence of quantum fluctuations of the electromagnetic (EM) field.In this letter, we layout such theory for a beam of neutral atoms and find an unusual new concept in interferometry: a non-local phase associated to pairs of paths rather than to individual ones. First, we present a theory of atomic phase-shifts taking the effect of field and atomic dipole fluctuations separately over each interferometer arm. This method already contains novel dynamical corrections, which cannot be obtained by standard techniques suitable for atoms driven by conservative forces. However, it neglects quantum correlations, mediated by the field, between the atomic wave-packets evolving along the separate arms. In order to capture this effect, we develop a theory of atom interferometers based on the influence functional method [6], which allows us to derive the non-Hamiltonian evolution of the external atomic observables after coarse-graining over the quantized electromagnetic field and internal atomic (dipole) degrees of freedom. A non-local phase shift arises as a consequence of the finite correlation time of dipole fluctuations interacting across a pair of interferometer paths. It is absent in the standard Hamiltonian treatment of matter-wave dynamics with conservative forces, which shows that the effect of quantum vacuum and zero-point dipole fluctuations on atomic waves cannot be understood as an effective potential.The influence functional method also allows one to consider the decoherence effect [7], another important conse-quence of the non-unitary nature of the matter-wave dynamics. However, in this letter we focus on the non-local real phase shifts beyond the expected loss of contrast in the fri...

We provide a Quantum Field Theory derivation of Lifshitz formula for the Casimir force due to a fluctuating real scalar field in d + 1 dimensions. The field is coupled to two imperfect, thick, plane mirrors, which are modeled by background potentials localized on their positions. The derivation proceeds from the calculation of the vacuum energy in the Euclidean version of the system, reducing the problem to the evaluation of a functional determinant. The latter is written, via Gelfand-Yaglom's formula, in terms of functions depending on the structure of the potential describing each mirror; those functions encode the properties which are relevant to the Casimir force and are the reflection coefficients evaluated at imaginary frequencies.

We develop an open-system dynamical theory of the Casimir interaction between coherent atomic waves and a material surface. The system -the external atomic waves -disturbs the environment -the electromagnetic field and the atomic dipole degrees of freedom -in a non-local manner by leaving footprints on distinct paths of the atom interferometer. This induces a non-local dynamical phase depending simultaneously on two distinct paths, beyond usual atom-optics methods, and comparable to the local dynamical phase corrections. Non-local and local atomic phase coherences are thus equally important to capture the interplay between the external atomic motion and the Casimir interaction. Such dynamical phases are obtained for finite-width wavepackets by developing a diagrammatic expansion of the disturbed environment quantum state.

We study non-superposition effects in the Dirichlet-Casimir interaction energy for N boundaries in d spatial dimensions, quantifying its departure from the case of an interaction where a superposition principle is valid. We first derive some general results about those effects, and then show that they become negligible only when the distances between surfaces are larger than the sizes of each individual surface. We consider different examples of this situation in one, two and three spatial dimensions. Finally, we present two examples, corresponding to highly symmetric configurations involving more than two surfaces. We show that, even though superposition is not valid, the total interaction energy may nevertheless be expressed as a sum of (non-Casimir) energies involving pairs of surfaces.

We discuss a fundamental property of open quantum systems: the quantum phases associated with their dynamical evolution are non-additive. We develop our argument by considering a multiplepath atom interferometer in the vicinity of a perfectly conducting plate. The coupling with the environment induces dynamical corrections to the atomic phases. In the specific example of a Casimir interaction, these corrections reflect the interplay between field retardation effects and the external atomic motion. Non-local open-system Casimir phase corrections are shown to be nonadditive, which follows directly from the unseparability of the influence functional describing the coupling of the atomic waves to their environment. This is an unprecedented feature in atom optics, which may be used in order to isolate non-local dynamical Casimir phases from the standard quasi-static Casimir contributions.Open quantum systems [1,2] have motivated a worldwide theoretical and experimental research effort. Basic quantum phenomenon such as decoherence [3] have been reported in a variety of mesoscopic systems. Atom interferometers [4] in the vicinity of a conducting surface constitute a particulary relevant and rich class of open quantum systems, in which both long-lived (atomic dipole) and short-lived (electric field) degrees of freedom are simultaneously at work.Here, we propose to use this example in order to demonstrate an unprecedented, key property of open quantum systems: the non-additivity of the quantum phases arising from their dynamical evolution. The coupling to the environment is described by an influence functional [5] depending simultaneously on a pair of quantum paths. This stands in sharp contrast to the quantum phases resulting from a unitary evolution, which depend only on single paths taken separately. While the phase differences associated to single-path contributions are additive by construction, the additivity has no reason to be valid for the influence functional phases associated to pairs of paths. In general, the doublepath influence functional phases cannot be separated into sums of single-path contributions [1]. The non-additivity of the environment-induced quantum phases is a direct consequence of this unseparability, which is intimately connected to the non-locality of these phases.Atom interferometers have been used to probe atomsurface interactions in the van der Waals (vdW) regime [6,7], turning atom optics into a promising field for the experimental investigation of dispersive forces [8][9][10][11][12][13]. The effect of surface interactions onto atomic waves propagating near a conducting plate is commonly described by means of the vdW (or Casimir-Polder at longer distances) potential taken at the instantaneous atomic position. In this description, the external atomic waves are treated as a closed quantum system driven by conservative forces.Nevertheless, we have shown recently [14] that such an approach is incomplete. This is so, because the external atomic degrees of freedom (d.o.f.s) are coupled to the ...