We clarify the controversy over the coherent-state (CS) versus the number-state (NS) pictures in quantum optics. The NS picture is equivalent to the CS picture, as long as the phases $ϕ$ in the laser fields are randomly distributed, as Mølmer argues [\pra {\bf 55}, 3195 (1997)]. However, the claim by Rudolph and Sanders [Phys. Rev. Lett. {\bf 87}, 077903 (2001)] has a few gaps. First, they make an assumption that is not necessarily true in the calculation of a density operator involved with a two-mode squeezed state. We show that there exists entanglement in the density operator without defying the assumption that phases are randomly distributed. Moreover, using a concept of picture-invariance, we argue that it is not that criteria for quantum teleportation are not satisfied. We discuss an analogy between the controversy on the CS versus NS pictures to that on the heliocentric versus geocentric pictures.
The Schrodinger and Heisenberg pictures are equivalent formulations of quantum mechanics. Here we use the Schrodinger picture to calculate the decoherence that occurs when an optical Schrodinger cat state is passed through a beam splitter. We find that an exponentially large amount of decoherence can occur even when there is a negligible change in the quadrature operator x(t) in the Heisenberg picture. Similar results have been observed in the decoherence produced by an optical amplifier, and we suggest that the usual quadrature operators in the Heisenberg picture do not provide a complete des…
The effective description of the weak interaction between an emitter and a bosonic field as a sequence of two-body collisions provides a simple intuitive picture compared to traditional quantum optics methods as well as an effective calculation tool of the joint emitter-field dynamics. Here, this collisional approach is extended to many emitters (atoms or resonators), each generally interacting with the field at many coupling points ("giant" emitter). In the regime of negligible delays, the unitary describing each collision in particular features a contribution of a chiral origin resulting in …
In this note we discuss the invariance under general changes of reference frame of all the physical predictions of particle detector models in quantum field theory in general and, in particular, of those used in quantum optics to model atoms interacting with light. We find explicitly how the light-matter interaction Hamiltonians change under general coordinate transformations, and analyze the subtleties of the Hamiltonians commonly used to describe the light-matter interaction when relativistic motion is taken into account.
We consider the most general scale invariant radial Hamiltonian allowing for anisotropic scaling between space and time. We formulate a renormalisation group analysis of this system and demonstrate the existence of a quantum phase transition from a continuous scale invariant phase to a discrete scale invariant phase. Close to the critical point, the discrete scale invariant phase is characterised by an isolated, closed, attracting trajectory in renomalisation group space (a limit cycle). Moving in appropriate directions in the parameter space of couplings this picture is altered to one control…
Super- and subradiance are usually described in the framework of Dicke collective states, which is an ``atomic picture'' in which the electromagnetic field only provides an effective interaction between the atoms. Here, we discuss a complementary picture, in which we describe the propagation and scattering of light in the atomic medium, which provides a complex susceptibility and scatterers. This ``optical picture'' is valid in the linear-optics regime for disordered samples and is mainly relevant at low density, when the susceptibility and scattering cross-section can be computed from simple …
We study all-optical signatures of the effective nonlinear couplings among electromagnetic fields in the quantum vacuum, using the collision of two focused high-intensity laser pulses as an example. The experimental signatures of quantum vacuum nonlinearities are encoded in signal photons, whose kinematic and polarization properties differ from the photons constituting the macroscopic laser fields. We implement an efficient numerical algorithm allowing for the theoretical investigation of such signatures in realistic field configurations accessible in experiment. This algorithm is based on a v…
We discuss how coherent driving of a two-level quantum system can be used to induce a complex phase on the ground state and we discuss its geometric and dynamic contributions. While the global phase of a wave function has no physical significance, coherent dynamics in a two-level subspace provides relative phases and is an essential building block for more advanced dynamics in larger systems. In this regard, we note that one must be careful with intuitive accounts of the phase dynamics as it depends on the interaction picture applied. To mitigate ambiguities in practical analyses, we suggest t…
We compare the predictions of the fundamentally motivated minimal coupling ($\hat{\boldsymbol{p}}\cdot\hat{\boldsymbol{A}}$) and the ubiquitous dipole coupling ($\hat{\boldsymbol{x}}\cdot\hat{\boldsymbol{E}}$) in the light-matter interaction. By studying the light-matter interaction for hydrogen-like atoms we find that the dipole approximation cannot be a-priori justified to analyze the physics of vacuum excitations (a very important phenomenon in relativistic quantum information) since a dominant wavelength is absent in those problems, no matter how small (as compared to any frequency scale) …
The conservation of physical quantities under coordinate transformations, known as gauge invariance, has been the foundation of theoretical frameworks in both quantum and classical theory. The finding of gauge-invariant quantities has enabled the geometric and topological interpretations of quantum phenomena with the Berry phase, or the separation of quark and gluon contributions in quantum chromodynamics. Here, with an example of quantum geometric quantities-Berry connection, phase, and curvature-we extract a new gauge-invariant quantity by applying a "weak value picture". By employing differ…
This work concerns the statistics of the Two-Time Measurement definition of heat variation in each reservoir of a thermodynamic quantum system. We study the cumulant generating function of the heat flows in the thermodynamic and large-time limits. It is well-known that, if the system is time-reversal invariant, this cumulant generating function satisfies the celebrated Evans--Searles symmetry. We show in addition that, under appropriate ultraviolet regularity assumptions on the local interaction between the reservoirs, it satisfies a translation-invariance property, as proposed in [Andrieux et…
