We revisit the back-action of emitted photons on the motion of the relative position of two cold atoms. We show that photon recoil resulting from the spontaneous emission can induce the localization of the relative position of the two atoms through the entanglement between the spatial motion of individual atoms and their emitted photons. The result provides a more realistic model for the analysis of the environment-induced localization of a macroscopic object.
We extend the beable interpretation, due to Bell, to the continuous spontaneous localization model (CSL). Results obtained by Vink are generalized to the modified Schrodinger equation of Ghirardi, Pearle and Rimini (GPR), which allows a beable interpretation for position and momentum.
A new proposal for a Lorentz-invariant spontaneous localization theory is presented. It is based on the choice of a suitable set of macroscopic quantities to be stochastically induced to have definite values. Such macroscopic quantities have the meaning of a time-integrated amount of a microscopically defined quantity called stuff related to the presence of massive particles.
In his recent paper [arXiv:1104.1938], Bedingham discussed a hybrid between a theory of spontaneous wave function collapse and Bohmian mechanics. I offer a simpler way of conveying the substance of Bedingham's paper.
For a solid lattice, we rederive the Continuous Spontaneous Localization (CSL) noise total energy gain of a test mass starting from a Lindblad formulation, and from a similar starting point rederive the geometry factor governing center of mass energy gain. We then suggest that the geometry factor can be used as a way to distinguish between low temperature cantilever motion saturation arising from CSL noise, and saturation arising from thermal leakage.
We describe a previously unexplored effect of the continuous spontaneous localization model whereby a correlation develops in the distributions of two nearby non-interacting particles following a period of diffusion. We propose the use of this effect as an experimental test differentiating between the continuous spontaneous localization model and standard quantum theory. The test involves building a joint probability distribution for the locations of the two particles by repeatedly releasing them from two nearby traps and subsequently measuring their positions after a brief period of time. We …
We propose to test the theory of continuous spontaneous localization (CSL) in an all-optical time-domain Talbot-Lau interferometer for clusters with masses exceeding 1000000 amu. By assessing the relevant environmental decoherence mechanisms, as well as the growing size of the particles relative to the grating fringes, we argue that it will be feasible to test the quantum superposition principle in a mass range excluded by recent estimates of the CSL effect.
The interaction of a moving charged particle with its coherent electromagnetic field is analysed in the framework of non-relativistic quantum mechanics. It is shown that, when this interaction is taken into account, a spatially localized state may have a mean energy lower than the one corresponding to a delocalized state.
The Continuous Spontaneous Localization (CSL) model strives to describe the quantum-to-classical transition from the viewpoint of collapse models. However, its original formulation suffers from a fundamental inconsistency in that it is explicitly energy non-conserving. Fortunately, a dissipative extension to CSL has been recently formulated that solves such energy-divergence problem. We compare the predictions of the dissipative and non-dissipative CSL models when various optomechanical settings are used, and contrast such predictions with available experimental data, thus building the corresp…
The Continuous Spontaneous Localization (CSL) model is the best known and studied among collapse models, which modify quantum mechanics and identify the fundamental reasons behind the unobservability of quantum superpositions at the macroscopic scale. Albeit several tests were performed during the last decade, up to date the CSL parameter space still exhibits a vast unexplored region. Here, we study and propose an unattempted non-interferometric test aimed to fill this gap. We show that the angular momentum diffusion predicted by CSL heavily constrains the parametric values of the model when a…
We investigate the effect of the Continuous Spontaneous Localization (CSL) model on light-pulse atom interferometry. Using a path-integral approach with an additional stochastic potential accounting for CSL, we derive an exponential loss of the contrast that scales linearly with the interferometer time $T$ if both interferometer arms are spatially separated. We compare our theoretical results with measurements from a cold rubidium atom interferometer based on counter-propagating two-photon transitions with pulse separation times up to $T$ = 260 ms and obtain the corresponding bounds on the CSL…
We propose a mathematical and a conceptual framework (called the `E-model' and the `event ontology' resp.) that encompasses and generalizes the `flash' ontology discussed in a recent paper by R. Tumulka (arXiv:quant-ph/0602208)
Working in the limit in which the localization length scale is large compared to other relevant length scales we examine three experimental situations with the continuous spontaneous localization (CSL) model---a well-motivated alternative to standard quantum theory. These are the two-slit experiment; scattering from a potential barrier; and the release of two non-interacting particles simultaneously from a potential trap. In each case we calculate the diagonal part of the time evolved density matrix giving a probability density function over final measured states. The case of the two-slit expe…
The spontaneous localization theory of Ghirardi, Rimini, and Weber (GRW) is a theory in which wavepacket reduction is treated as a genuine physical process. Here it is shown that the mathematical formalism of GRW can be given an interpretation in terms of an evolving distribution of particles on configuration space similar to Bohmian mechanics (BM). The GRW wavefunction acts as a pilot wave for the set of particles. In addition, a continuous stream of noisy information concerning the precise whereabouts of the particles must be specified. Nonlinear filtering techniques are used to determine th…
Paul traps are ion traps that are widely used in spectroscopic experiments to confine and stabilize a charged particle within a small region using oscillating electric fields. The dynamics of the particle inside a Paul trap is described by Mathieu equations. It has been proposed that such traps can be used to detect the effects produced by spontaneous collapse of the associated wavefunction, as described by the model of CSL (Continuous Spontaneous Localization). This model is a non-linear, stochastic and non-relativistic modification to the Schrödinger equation which predicts an additional ran…
We give an explicit stochastic Hamiltonian model of discontinuous unitary evolution for quantum spontaneous jumps like in a system of atoms in quantum optics, or in a system of quantum particles that interacts singularly with "bubbles" which admit a continual counting observation. This model allows to watch a quantum trajectory in a photodetector or in a cloud chamber by spontaneous localisations of the momentums of the scattered photons or bubbles. Thus, the continuous reduction and spontaneous localization theory is obtained from a Hamiltonian singular interaction as a result of quantum filt…
Energy diffusion due to spontaneous localization (SL) for a relativistically-fast moving particle is examined. SL is an alternative to standard quantum theory in which quantum state reduction is treated as a random physical process which is incorporated into the Schrödinger equation in an observer-independent way. These models make predictions in conflict with standard quantum theory one of which is non conservation of energy. On the basis of proposed relativistic extensions of SL it is argued that for a single localized particle, non-relativistic SL should remain valid in the rest frame of th…
Collapse models explain the absence of quantum superpositions at the macroscopic scale, while giving practically the same predictions as quantum mechanics for microscopic systems. The Continuous Spontaneous Localization (CSL) model is the most refined and studied among collapse models. A well-known problem of this model, and of similar ones, is the steady and unlimited increase of the energy induced by the collapse noise. Here we present the dissipative version of the CSL model, which guarantees a finite energy during the entire system's evolution, thus making a crucial step toward a realistic…
Matter-wave interferometry is a direct test of the quantum superposition principle for massive systems, and of collapse models. Here we show that the bounds placed by matter-wave interferometry depend weakly on the details of the collapse mechanism. Specifically, we compute the bounds on the CSL model and its variants, provided by the the KDTL interferometry experiment of Arndt's group [Phys. Chem. Chem. Phys., 2013, 15, 14696-14700], which currently holds the record of largest mass in interferometry. We also show that the CSL family of models emerges naturally by considering a minimal set of …
We apply the formalism of quantum estimation theory to extract information about potential collapse mechanisms of the continuous spontaneous localisation (CSL) form. In order to estimate the strength with which the field responsible for the CSL mechanism couples to massive systems, we consider the optomechanical interaction between a mechanical resonator and a cavity field. Our estimation strategy passes through the probing of either the state of the oscillator or that of the electromagnetic field that drives its motion. In particular, we concentrate on all-optical measurements, such as homody…
On the basis of a proposed model of wave function collapse, we investigate spontaneous localization of a quantum state. The model is similar to the Ghirardi-Rimini-Weber model, while we postulate the localization functions to depend on the quantum state to suffer collapse. According to the model, dual dynamics in quantum mechanics, deterministic and stochastic time evolution, are algorithmically implemented in tandem. After discussing the physical implications of the model qualitatively, we present numerical results for one-dimensional systems by way of example.
We investigate the dynamical behavior of the atom-photon entanglement in a V-type three-level quantum system using the atomic reduced entropy. It is shown that an atom and photons are entangled at the steady-state; however disentanglement can also be achieved in an especial condition. It is demonstrated that in the presence of quantum interference induced by spontaneous emission, the reduced entropy and the atom-photon entanglement are phase-dependent. Non-stationary solution is also obtained when the quantum interference due to the spontaneous emission is completely included.
We find an analogy between turbulence and the dynamics of the continuous spontaneous localization model (CSL) of the wave function. The use of a standard white noise in the localization process gives Richardson's t^3 law for the turbulent diffusion, while the introduction of an affine noise in the CSL allows us to obtain the intermittency corrections to this law.
There is a striking convergence between Burgers turbulence and the continuous spontaneous localization [CSL] model of quantum mechanics. In this paper, we exploit this analogy showing the similarities in the physics of these two apparently unrelated problems. It is hoped that the kind of analogy we introduce here may lead to important developments in both areas.
Using the Born expansion of the Green tensor, we consider the spontaneous decay rate of an excited atom placed in the vicinity of a rectangular plate. We discuss the limitations of the commonly used simplifying assumption that the plate extends to infinity in the lateral directions and examine the effects of the atomic dipole moment orientation, atomic position, and plate boundary and thickness on the atomic decay rate. In particular, it is shown that in the boundary region, the spontaneous decay rate can be strongly modified.
A recent experiment [K. C. Lee et al., Science 334, 1253 (2011)] succeeded in detecting entanglement between two macroscopic specks of diamonds, separated by a macroscopic distance, at room temperature. This impressive results is a further confirmation of the validity of quantum theory in (at least parts of) the mesoscopic and macroscopic domain, and poses a challenge to collapse models, which predict a violation of the quantum superposition principle, which is the bigger the larger the system. We analyze the experiment in the light of such models. We will show that the bounds placed by experi…
We derive spontaneous emission rate and line shift for two-level atoms coupled to the radiation field using causal perturbation theory. In this approach, employing the theory of distribution splitting prevents the occurrence of divergent integrals. Our method confirms the result for atomic decay rate but suggests that the cutoff frequency for the atomic line shift is determined by the atomic mass, rather than Bohr radius or electron mass.
Two recent experiments studying the potential effect of entanglement on the emission properties of excited atoms produced in molecular photodissociation have been interpreted in conflicting ways. We present a theoretical analysis of the problem, showing that the experimental results can be explained by a combination of three processes: entanglement, exchange effects associated with the identical nature of the atoms and disentanglement by spontaneous emission. According to our approach these experiments provide the first verification of the phenomenon of disentanglement by spontaneous emission.
The Continuous Spontaneous Localization (CSL) model predicts a tiny break of energy conservation via a weak stochastic force acting on physical systems, which triggers the collapse of the wave function. Mechanical oscillators are a natural way to test such a force; in particular levitated micro-mechanical oscillator has been recently proposed to be an ideal system. We report a proof-of-principle experiment with a micro-oscillator generated by a micro-sphere diamagnetically levitated in a magneto-gravitational trap under high vacuum. Due to the ultra-low mechanical dissipation, the oscillator p…
An electronically excited atom or molecule located outside but near a planar optical waveguide can decay by spontaneous emission of a photon into a guided mode of the waveguide. We outline a QED theory for calculating the probability for this process and describe general physical insights from that theory. A couple of representative examples are discussed in detail.
Spontaneous Raman processes in cold atoms have been widely used in the past decade for generating single photons. Here, we present a method to optimize their efficiencies for given atomic coherences and optical depths. We give a simple and complete recipe that can be used in present-day experiments, attaining near-optimal single photon emission while preserving the photon purity.
We study evolution of entanglement of two two-level atoms in the presence of dissipation caused by spontaneous emission. We find explicit fromulas for the amount of entanglement as a function of time, in the case of destruction of the initial entanglement and possible creation of a transient entanglement between atoms. We also discuss how spontaneous emission influences nonlocality of states expressed by violation of Bell - CHSH inequality. It is shown that evolving system very quickly becomes local, even if entanglement is still present or produced.
We propose a dissipative scheme to prepare a three-dimensional entangled state for two atoms trapped in separate coupled cavities. Our work shows that both atomic spontaneous emission and cavity decay, which are two typical obstacles in unitary-dynamics-based schemes, could be utilized as resources for high-dimensional entangled state preparation without specifying initial state and controlling time precisely. Final numerical simulation with one group of experimental parameters indicates that the performance of our scheme is better than the unitary-dynamics-based scheme.
Here we discuss an effect of dephasing induced by a weak gravitational field on the collective radiation dynamics of an atomic system in timed single-photon Dicke states. We show that a photon absorbed by the stationary system of randomly placed stationary atoms is no longer spontaneously emitted in the direction of the impinging photon. Gravity leads to broadening of the angular distribution of emission.
A more detailed analysis of the measurement problem continues to support the position taken by Shimony and the author that collapse of the wave function takes place in an objective manner in the rhodopsin molecule of the retina. This casts further doubts on the theories involving a spontaneous localization collapse process or a no-collapse decoherence process taking place in the visual cortex in a subjective fashion. The possibility is then raised, as per Anandan, as to whether the solution of the measurement problem in quantum theory allows one to address the problem of quantizing gravitation…
We investigate the spontaneous emission from an inverted Y-type atomic system coupled by three coherent fields. We use the Schrödinger equation to calculate the probability amplitudes of the wave function of the system and derive an analytical expression of the spontaneous emission spectrum to trace the origin of the spectral features. Quantum interference effects, such as the spectral line narrowing, spectrum splitting and dark resonance are observed. The number of spectral components, the spectral linewidth, and relative heights can be very different depending on the physical parameters. A v…
We study quantum teleportation via two two-level atoms coupled collectively to a multimode vacuum field and prepared initially in different atomic states. We concentrated on influence of the spontaneous emission, collective damping and dipole-dipole interaction of the atoms on fidelity dynamics of quantum teleportation and obtained the region of spatial distance between the two atoms over which the state can be teleported nonclassically. Moreover, we showed through concrete examples that entanglement of the channel state is the prerequisite but not the only essential quantity for predicting th…
Analysis of the spontaneously induced correlation on atom-radiation entanglement in an ensemble of two-level atoms initially prepared in the upper level and placed in a cavity containing a squeezed radiation employing the method of evaluating the coherent-state propagator is presented. It is found that the cavity radiation exhibits squeezing which is directly attributed to the squeezed radiation in the cavity. The intensity of the cavity radiation increases with the squeeze parameter and interaction time. It is also shown that substantial degree of entanglement between the atomic states and ra…
We discuss a simple example demonstrating that spontaneous emission from "space-time-superposed" atomic center-of-mass wave packets is nontrivially and time-dependent modified with respect to the standard dipole-pattern typical of "space-superposed" wave packets. Our approach provides an approximate description of a nonsimultaneous interaction of electromagnetic field with different parts of a wave packet.
We report an interference experiment of spontaneous emission of light from two distant solid-state ensembles of atoms that are coherently excited by a short laser pulse. The ensembles are Erbium ions doped into two LiNbO3 crystals with channel waveguides, which are placed in the two arms of a Mach-Zehnder interferometer. The light that is spontaneously emitted after the excitation pulse shows first-order interference. By a strong collective enhancement of the emission, the atoms behave as ideal two-level quantum systems and no which-path information is left in the atomic ensembles after emissi…
We study the spontaneous emission of an excited atom close to an optical nanofiber and the resulting scattering forces. For a suitably chosen orientation of the atomic dipole, the spontaneous emission pattern becomes asymmetric and a resonant Casimir--Polder force parallel to the fiber axis arises. For a simple model case, we show that the such a lateral force is due to the interaction of the circularly oscillating atomic dipole moment with its image inside the material. With the Casimir--Polder energy being constant in the lateral direction, the predicted lateral force does not derive from a …
We study a quantum electrodynamics (QED) system made of an two-level atom and a semi-infinite rectangular waveguide, which behaves as a perfect mirror in one end. The spatial dependence of the atomic spontaneous emission has been included in the coupling strength relevant to the eigenmodes of the waveguide. The role of retardation is studied for the atomic transition frequency far away from the cutoff frequencies. The atom-mirror distance introduces different phases and retardation times into the dynamics of the atom interacting resonantly with the corresponding transverse modes. It is found t…
We study the collective spontaneous emission of three identical two-level atoms initially prepared in the excited states by measuring Glauber's third-order photon correlation function. Assuming two atoms at sub-wavelength distance from each other such that they are subject to the dipole-dipole interaction while the third one is located several wavelengths away, we observe super- and subradiant decay alike, depending on the direction of observation. Unlike the case where no remote atom is introduced or no conditional measurements are performed, the spontaneous emission behavior of the condition…
We report on numerical calculations of the spontaneous emission rate of a Rydberg-excited sodium atom in the vicinity of an optical nanofibre. In particular, we study how this rate varies with the distance of the atom to the fibre, the fibre's radius, the symmetry s or p of the Rydberg state as well as its principal quantum number. We find that a fraction of the spontaneously emitted light can be captured and guided along the fibre. This suggests that such a setup could be used for networking atomic ensembles, manipulated in a collective way due to the Rydberg blockade phenomenon.
We investigate spontaneous emission of a two-level atom with an arbitrarily polarized electric dipole in front of a flat dielectric surface. We treat the general case where the atomic dipole matrix element is a complex vector, that is, the atomic dipole can rotate with time in space. We calculate the rates of spontaneous emission into evanescent and radiation modes and study the angular densities of the rates in the space of wave vectors for the field modes. We show that, when the ellipticity of the atomic dipole is not zero, the angular density of the spontaneous emission rate of the atom may…
We present a scheme for two-dimensional (2D) atom localization in a three-level atomic system. The scheme is based on quantum coherence via classical standing wave fields between the two excited levels. Our results show that conditional position probability is significantly phase dependent of the applied field and frequency detuning of spontaneously emitted photons. We obtain a single localization peak having probability close to unity by manipulating the control parameters. The effect of atomic level coherence on the sub-wavelength localization has also been studied. Our scheme may be helpful…
In this paper we consider an initially excited two-level system coupled to a monomode cavity, and compute exact expressions for the spectra spontaneously emitted by each system in the general case where they have arbitrary linewidths and frequencies. Our method is based on the fact that this problem has an easily solvable classical counterpart, which provides a clear interpretation of the evidenced phenomena. We show that if the cavity linewidth is much lower than the atomic linewidth, photons are emitted at the cavity frequency, even if the atom and the cavity are strongly detuned. We also st…
In spontaneous emission an atom in an excited state undergoes a transition to the ground state and emits a single photon. Associated with the emission is a change of the atomic momentum due to photon recoil. Photon emission can be modified close to surfaces and in cavities. For an ion, localized in front of a mirror, coherence of the emitted resonance fluorescence has been reported. In free space experiments demonstrated that spontaneous emission destroys motional coherence. Here we report on motional coherence created by a single spontaneous emission event close to a mirror surface. The coher…
Collapse models describe phenomenologically the quantum-to-classical transition by adding suitable nonlinear and stochastic terms to the Schroedinger equation, thus (slightly) modifying the dynamics of quantum systems. Experimental bounds on the collapse parameters have been derived from various experiments involving a plethora of different systems, from single atoms to gravitational wave detectors. Here, we give a comprehensive treatment of the Continuous Spontaneous Localization (CSL) model, the most studied among collapse models, for Fermi liquids. We consider both the white and non-white n…
Starting from the quantized version of Maxwell's equations for the electromagnetic field in an arbitrary linear Kramers-Kronig dielectric, spontaneous decay of the excited state of a two-level atom embedded in a dispersive and absorbing medium is studied and the decay rate is calculated. The calculations are performed for both the (Clausius-Mosotti) virtual cavity model and the (Glauber-Lewenstein) real cavity model. It is shown that owing to nonradiative decay associated with absorption the rate of spontaneous decay sensitively depends on the cavity radius when the atomic transition frequency…
Tunable interaction between two atoms in a cavity is realized by interacting the two atoms with an extra controllable single-mode squeezed field. Such a controllable interaction can be further used to control entanglement between the two atoms against amplitude damping decoherence caused by spontaneous emissions. For the independent amplitude damping decoherence channel, entanglement will be lost completely without controls, while it can be partially preserved by the proposed strategy. For the collective amplitude damping decoherence channel, our strategy can enhance the entanglement compared …
We study spontaneous radiative decay of translational levels of an atom in the vicinity of a semi-infinite dielectric. We systematically derive the microscopic dynamical equations for the spontaneous decay process. We calculate analytically and numerically the radiative linewidths and the spontaneous transition rates for the translational levels. The roles of the interference between the emitted and reflected fields and of the transmission into the evanescent modes are clearly identified. Our numerical calculations for the silica--cesium interaction show that the radiative linewidths of the bo…
We study spontaneously generated entanglement (SGE) between two identical multilevel atoms in free space via vacuum-induced radiative coupling. We show that the SGE in two-atom systems may initially increase with time but eventually vanishes in the time scale determined by the excited state lifetime and radiative coupling strength between the two atoms. We demonstrate that a steady-state SGE can be established by incoherently pumping the excited states of the two-atom system. We have shown that an appropriate rate of incoherent pump can help producing optimal SGE. The multilevel systems offer …
We study the influence of the distribution of atoms on the cooperative spontaneous emission by a simple model of three identical atoms. The effects of counter rotating terms are included by a unitary transformation method. By discussing two special cases that the three atoms are arranged as an equilateral triangle and in a straight line, we find that the superradiance of the coherent system largely dependent on the homogeneity of the atoms' distribution. If the atoms distribute symmetrically, the superradiant emission will be enhanced. Next, we calculate the emission spectra of three identical…
Spontaneous emission and Lamb shift of atoms in absorbing dielectrics are discussed. A Green's-function approach is used based on the multipolar interaction Hamiltonian of a collection of atomic dipoles with the quantised radiation field. The rate of decay and level shifts are determined by the retarded Green's-function of the interacting electric displacement field, which is calculated from a Dyson equation describing multiple scattering. The positions of the atomic dipoles forming the dielectrics are assumed to be uncorrelated and a continuum approximation is used. The associated unphysical …
