Physical Review A

We propose three criteria for identifying continuous variable entanglement between two many-particle systems with no restrictions on the quantum state of the local oscillators used in the measurements. Mistakenly asserting a coherent state for the local oscillator can lead to incorrectly identifying...

We calculate the Casimir interaction between two short-range scatterers embedded in a background of one-dimensional massless Dirac fermions using a force-operator approach. We obtain the force between two finite-width square barriers and take the limit of zero width and infinite potential strength t...

We propose a complete tomographic reconstruction of vortex states carrying orbital angular momentum. The scheme determines the angular probability distribution of the state at different times under free evolution. To represent the quantum state, we introduce a bona fide Wigner function defined on th...

We analyze the decoherence induced on a single qubit by the interaction with a two-level boson system with critical internal dynamics. We explore how the decoherence process is affected by the presence of quantum phase transitions in the environment. We conclude that the dynamics of the qubit change...

We introduce a measure to quantify the non-Gaussian character of a quantum state: the quantum relative entropy between the state under examination and a reference Gaussian state. We analyze in detail the properties of our measure and illustrate its relationships with relevant quantities in quantum i...

We highlight the direct link between the time-dependent entanglement and single-qubit excited-state population for two independent qubits, each coupled to a zero-temperature bosonic environment. We show that, in environments structured so as to inhibit spontaneous emission, entanglement trapping and...

We present a method to determine the decay of multiparticle quantum correlations as quantified by the geometric measure of entanglement under the influence of decoherence. With this, we compare the robustness of entanglement in Greenberger-Horne-Zeilinger (GHZ), cluster, W , and Dicke states of fou...

We study atom-ion scattering in the ultracold regime. To this aim, an analytical model based on the multichannel quantum-defect formalism is developed and compared to close-coupled numerical calculations. We investigate the occurrence of magnetic Feshbach resonances, focusing on the specific ⁴⁰Ca⁺+...

We study two ions confined in a Penning trap. We show that electronically highly excited states exist in which an electron is delocalized among the two ions forming a giant molecule of several micrometer size. At energies close to the top of the Coulomb barrier, these molecular states can be regarde...

We present a joint experimental and theoretical study of spin depolarization in collisions of alkali-metal atoms with ³He in a magnetic field. A rigorous quantum theory for spin-changing transitions is developed and applied to calculate the spin exchange and spin relaxation rates of Li and K atoms...

We provide evidence for the dipole blockade of Rydberg excitation by examining the distributions of the number of Rydberg excitations created in ensembles of interacting Rydberg atoms. We show that, over a range of densities, the Rydberg excitation number distributions become significantly narrower ...

We combined adaptive closed-loop optimization, phase shaping with a restricted search space, and imaging to control dynamics and decipher the optimal pulse. The approach was applied to controlling the amplitude of the CO₂ bending vibration during strong-field Coulomb explosion. The search space wa...

We observe high-order harmonic spectra generated from a thin atomic medium, Ar, Kr, and Xe, by intense 800-nm and 1300-nm femtosecond pulses. A clear signature of a single-atom response is observed in the harmonic spectra. Especially in the case of Ar, a Cooper minimum, reflecting the electronic...

We investigate the effect of the anisotropy of a harmonic trap on the behavior of a fast rotating Bose-Einstein condensate. Fast rotation is reached when the rotational velocity is close to the smallest trapping frequency, thereby deconfining the condensate in the corresponding direction. We charact...

We identify a one-dimensional supersolid phase in a binary mixture of near-hard-core bosons with weak, local interspecies repulsion. We find realistic conditions under which such a phase, defined here as the coexistence of quasisuperfluidity and quasi-charge-density-wave order, can be produced and o...

A method to create paired-atom laser beams from a metastable helium atom laser via four-wave mixing is demonstrated. Radio-frequency outcoupling is used to extract atoms from a Bose-Einstein condensate near the center of the condensate and initiate scattering between trapped and untrapped atoms. The...

We theoretically explore the generation of few-body analogs of fractional quantum Hall states. We consider an array of identical few-atom clusters (n=2,3,4) , each cluster trapped at the node of an optical lattice. By temporally varying the amplitude and phase of the trapping lasers, one can introd...

We investigate the time taken for global collapse by a dipolar Bose-Einstein condensate. Two semianalytical approaches and exact numerical integration of the mean-field dynamics are considered. The semianalytical approaches are based on a Gaussian ansatz and a Thomas-Fermi solution for the shape of ...

We study the phase diagram of the mixture of a Bose-Einstein condensate and a two-component Fermi gas. In particular, we identify the regime where the homogeneous system becomes unstable against phase separation. We show that, under proper conditions, the phase-separation phenomenon can be exploited...

We have observed the stationary interference oscillations of a triple-entangled neutron state in an interferometric experiment. Time-dependent interaction with two radio-frequency fields enables coherent manipulation of an energy degree of freedom in a single neutron. The system is characterized by ...

Quantum systems in Fock states do not have a phase. When two or more Bose-Einstein condensates are sent into interferometers, they nevertheless acquire a relative phase under the effect of quantum measurements. The usual explanation relies on spontaneous symmetry breaking, where phases are ascribed ...

It is shown how the total internal reflection of orbital-angular-momentum-endowed light can lead to the generation of evanescent light possessing rotational properties in which the intensity distribution is firmly localized in the vicinity of the surface. The characteristics of these surface optical...

We study the effects of realistic dephasing environments on a pair of solid-state single-photon sources in the context of the Hong-Ou-Mandel dip. By means of solutions for the Markovian or exact non-Markovian dephasing dynamics of the sources, we show that the resulting loss of visibility depends cr...

We investigate the effects of rotation about the axis of an astigmatic two-mirror cavity on its optical properties. This simple geometry constitutes an optical system that can be destabilized and, more surprisingly, stabilized by rotation. As such, it has some similarity with both the Paul trap and ...

We theoretically study classical step-modulated pulse propagation in an optically thick medium with electromagnetically induced transparency (EIT) using a fast Fourier transform and a proposed hybrid-asymptotic analysis. The 100% transmitted leading edge traveling at c consists of Sommerfeld-Brill...

We present an analytic perturbation theory which extends the paraxial approximation for a common cylindrically symmetric stable optical resonator and incorporates the differential, polarization-dependent reflectivity of a Bragg mirror. The degeneracy of Laguerre-Gauss modes with distinct orbital ang...

We show that a 40-μm -diameter vertical-cavity surface-emitting laser (VCSEL) is capable of supporting spatially localized structures with linear polarization, orthogonal to the principal polarization. The VCSEL is biased above the lasing threshold and emits a well-defined linear polarization (pri...

We demonstrate weak and strong regimes of optical spatial turbulence by considering the nonlinear interaction of three partially coherent spatial beams. The geometry represents a multiple bump-on-tail instability, allowing an interpretation of nonlinear statistical light as a photonic plasma. For we...

Both analytical and numerical investigation of the structural features of ultrashort-laser-pulse self-focusing is presented. The analysis is performed under sufficiently general assumptions concerning the medium dispersion. It is demonstrated that the wave-field self-focusing proceeds with overtakin...

Ghost-imaging experiments correlate the outputs from two photodetectors: a high spatial-resolution (scanning pinhole or charge-coupled-device camera) detector that measures a field which has not interacted with the object to be imaged and a bucket (single-pixel) detector that collects a field that h...

We study atom-ion scattering in the ultracold regime. To this aim, an analytical model based on the multichannel quantum-defect formalism is developed and compared to close-coupled numerical calculations. We investigate the occurrence of magnetic Feshbach resonances, focusing on the specific ⁴⁰Ca⁺+...

The effects of strong magnetic fields (B∼10⁴   T) on charge exchange, excitation, and ionization processes in collisions of H(1s) atoms with fully stripped ions A^Z+ are studied by the classical trajectory Monte Carlo method in the energy range 25–2000   keV∕u . The cases B⃗...

Mutually unbiased bases encapsulate the concept of complementarity—the impossibility of simultaneous knowledge of certain observables—in the formalism of quantum theory. Although this concept is at the heart of quantum mechanics, the number of these bases is unknown except for systems of dimensi...

I explore entanglement dynamics in a three qubit system comparing the ability of entanglement witnesses to detect tripartite entanglement to the phenomenon of entanglement sudden death (ESD). Using a system subject to dephasing I invoke entanglement witnesses to detect tripartite Greenberger-Horne-Z...

We show, in the context of quantum combinatorial optimization, or quantum annealing, how the nonlinear Schrödinger-Langevin-Kostin equation can dynamically drive the system toward its ground state. We illustrate, moreover, how a frictional force of Kostin type can prevent the appearance of genuinel...

We consider, within the algebraic formalism, the time dependence of fidelity for qubits encoded in an open physical system. We relate the decay of fidelity to the evolution of correlation functions and, in the particular case of a Markovian dynamics, to the spectral gap of the generator of the semig...

Controlled measurement processes with high fidelity and robustness will be of substantial interest to fundamental quantum studies as well as quantum-information processing. This work proposes a simple scheme to realize controlled measurements of the state of a single spin, via controlled quantum sig...

By confining pairs of ions in a Penning trap, and alternating each ion between large and small cyclotron orbits, we have measured the cyclotron frequency ratios ¹²CD₃⁺∕¹⁸O⁺ , ¹²C₂D₆⁺∕¹⁸O₂⁺ , ¹²C₃⁺∕¹⁸O₂⁺ , ¹³CD₃⁺∕¹⁹F⁺ , and ²⁸SiH₃⁺∕¹²C¹⁹F⁺ . Combined with other measurements for H, D, ^...

Analytical calculations show that the mean motion of a quantum particle trapped by a rapidly oscillating potential can be significantly manipulated by inducing phase hops—i.e., by instantaneously changing the potential’s phase. A phase hop can be visualized as being the result of a collision wit...

An efficient method for the numerical solution of a non-Markovian, open-system density matrix equation of motion in coordinate representation is developed. We apply the scheme to model simulations of the laser-assisted O+H→OH association reaction in an environment. The suggested approach is base...

We investigate the possible form of ideal intersections for two-dimensional rf trap networks suitable for quantum information processing with trapped ions. We show that the lowest order multipole component of the rf field that can contribute to an ideal intersection is a hexapole term uniquely deter...

We combined adaptive closed-loop optimization, phase shaping with a restricted search space, and imaging to control dynamics and decipher the optimal pulse. The approach was applied to controlling the amplitude of the CO₂ bending vibration during strong-field Coulomb explosion. The search space wa...

Spectral line shapes in hot plasmas submitted to a strong oscillating electric field have been theoretically studied by applying the standard hypotheses of plasma line broadening together with a nonperturbative Floquet treatment of the external oscillating field. The formulation has been applied to ...

Some practical improvements are proposed for the “optical-shaker” laser-cooling technique [I. S. Averbukh and Y. Prior, Phys. Rev. Lett. 94, 153002 (2005)]. The improved technique results in an increased cooling rate and decreases the minimum cooling temperature achievable with the optical shake...

We study a model for electron detachment from negative ions by ultrashort unipolar electric pulses. The electron-atom interaction is described by the zero-range potential and the temporal dependence of the electric field is approximated by the Dirac δ functions. The case of a single pulse can be ...

We report on the experimental observation of dynamic localization of a Bose-Einstein condensate in a shaken optical lattice, both for sinusoidal and square-wave forcing. The formulation of this effect in terms of a quasienergy band collapse, backed by the excellent agreement of the observed collapse...

We discuss various superfluid properties of a two-component Fermi system in the presence of a tight one-dimensional periodic potential in a three-dimensional system. We use zero temperature mean field theory and derive analytical expressions for the Josephson current, the sound velocity, and the cen...

We demonstrate that superradiance and collective atomic recoil lasing from cold atoms can be enhanced using a two-frequency pump with frequency difference twice the two-photon recoil frequency ω_r . In the good-cavity regime the atoms behave as a three-recoil-level system, collectively scattering a...

We work out two different analytical methods for calculating the boundary of the Mott-insulator–superfluid (MI-SF) quantum phase transition for scalar bosons in cubic optical lattices of arbitrary dimension at zero temperature which improve upon the seminal mean-field result. The first one is a va...

Based on standard field-theoretic considerations, we develop an effective action approach for investigating quantum phase transitions in lattice Bose systems at arbitrary temperature. We begin by adding to the Hamiltonian of interest a symmetry breaking source term. Using time-dependent perturbation...

The nonlinear coupled Gross-Pitaevskii equation governing the dynamics of the two-component Bose-Einstein condensate (TBEC) is shown to admit sinusoidal, propagating-wave solutions in quasi-one-dimensional geometry in a trap. The solutions exist for a wide parameter range, which illustrates a proced...

Hard x-ray phase-contrast imaging provides high sensitivity to weakly absorbing low- Z objects in medicine, biology, and materials science. Here, we describe a feasible method to obtain differential phase-contrast images directly with incoherent x-ray sources, avoiding the Talbot effect, which requ...

We investigate the formation and coupling of defect modes in two-dimensional photonic crystal (PC) band gaps associated with degenerate edges. Using a method based on Green’s functions and perturbation theory, we derive a condition for the degeneracy of a defect mode in a PC band gap. We show that...

Using the Madelung transformation we show that in a quantum free-electron laser the beam obeys the equations of a quantum fluid in which the potential is the classical potential plus a quantum potential. The classical limit is shown explicitly.

In a recent paper (Phys. Rev. A78, 020101(R) (2008)), Kim et al. have reported a large anomaly in the scaling law of the electrostatic interaction between a sphere and a plate, which was observed during the calibration of their Casimir force set-up. Here we experimentally demonstrate that this behavior is not universal. Electrostatic calibrations obtained with our set-up follow the scaling law expected from elementary electrostatic arguments, even when the electrostatic voltage that one must apply to minimize the force (typically ascribed to contact potentials) depends on the separation between the surfaces.

We analyze the dynamics of a system qudit of dimension m sequentially interacting with the n-dimensional qudits of a chain playing the role of an environment. Each pairwise collision has been modeled as a random unitary transformation. The relaxation to equilibrium of the purity of the system qudit, averaged over random collisions, is analytically computed by means of a Markov chain approach. In particular, we show that the steady state is the one corresponding to the steady state for random collisions with a single environment qudit of effective dimension ne=nm. Finally, we numerically investigate aspects of the entanglement dynamics for qubits (m = n = 2) and show that random unitary collisions can create multipartite entanglement between the system qudit and the qudits of the chain.

We study the violation of the Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) inequality for two spin systems, of arbitrary spins , prepared in an entanglement of spin coherent states of each of the spins. We show that the Bell-CHSH inequality is quite robustly violated for a wide range of values of the parameters that specify the spin coherent states, and, for a particular choice of these parameters, maximal violations are obtained. That is, the violations can reach the Tsirelson bound, for any choices of the spins.

We propose a tomography scheme capable of reconstructing the quantum state of an unknown mode of light. The complex mode structure of the investigated field is expressed by a single number - the mismatch between the probe and signal. This parameter is estimated as a part of the quantum tomography protocol. This opens new ways for reconstructions utilizing interference between independent sources.

We present a polymer quantization of the -l/r2 potential on the positive real line and compute numerically the bound state eigenenergies in terms of the dimensionless coupling constant l. The singularity at the origin is handled in two ways: first, by regularizing the potential and adopting either symmetric or antisymmetric boundary conditions; second, by keeping the potential unregularized but allowing the singularity to be balanced by an antisymmetric boundary condition. The results are compared to the semiclassical limit of the polymer theory and to the conventional Schrödinger quantization on L2(\mathbbR+). The various quantization schemes are in excellent agreement for the highly excited states but differ for the low-lying states, and the polymer spectrum is bounded below even when the Schrödinger spectrum is not. We find as expected that for the antisymmetric boundary condition the regularization of the potential is redundant: the polymer quantum theory is well defined even with the unregularized potential and the regularization of the potential does not significantly affect the spectrum.

We explore how entanglement of a bipartite system evolves when one subsystem undergoes the action of an arbitrary noisy channel. It is found that the dynamics of entanglement of such system is determined by the channel's action on the maximally entangled state, which includes as a special case the results for two-qubit systems [Nature Physics 4, 99 (2008)]. In particular, for multi-qubit or qubit-qudit systems, we get a general factorization law for evolution equation of entanglement with one qubit being subject to a noisy channel.

So far, various multi-photon entangled states have been observed experimentally by using different experimental set-ups. Here, we present a scheme to realize many SLOCC-inequivalent states of three and four qubits via projective measurements on suitable entangled states. We demonstrate how these states can be observed experimentally in a single set-up and study the feasibility of the implementation with present-day technology.

We propose a scheme to produce continuous variable entanglement between phase-quadrature amplitudes of two light modes in optomechanical system. For proper driving power and detuning, the entanglement is insensitive with bath temperature and Q of mechanical oscillator. Under realistic experimental conditions, we find that the entanglement could be very large even at room temperature.

We investigate the build-up of quasi-long-range order in the XX chain with transverse magnetic field at finite size. As the field is varied, the ground state of the system displays multiple level crossings producing a sequence of entanglement jumps. Using the partial fidelity and susceptibility, we study the transition to the thermodynamic limit and argue that the topological order can be described in terms of kink-antikink pairs and marked by edge spin entanglement.

We report both experimental and theoretical studies on x-ray absorption measured using partial Auger yields of gas phase nitrogen, carbon monoxide, and oxygen molecules near the N1sp*, O1sp*, and O1sp* regions, respectively. The main tool of our study is a two-dimensional map in which resonant Auger yields are plotted as a function of photon and kinetic energy. The partial yields of the three molecules are analyzed in detail by extracting profiles along various directions in the map. Narrowing of the absorption resonances is observed along the direction of constant kinetic energy. It is shown that such profiles are similar to the conventional x-ray absorption spectrum for a broad class of molecules whose potential energy surfaces of the final and core-excited states are almost parallel. However, substantial differences with the conventional x-ray absorption profiles are observed in the general case of non-parallel surfaces due to the lifetime vibrational interference. Here, we suggest a systematic way to eliminate the lifetime vibrational interference.

In the photoelectron spectrum of N2 the apparent ionization energy to form the B2Su+ state increases linearly with the photon energy. Rotationally resolved measurements of the fluorescent decay of this state show a linear increase of rotational heating with increasing photon energy. These results are in quantitative agreement with the prediction of the theory of recoil-induced rotational excitation, indicating that the rotational heating that has been observed previously arises primarily from such recoil-induced excitation. Together with other results that have been reported they show that recoil-induced internal excitation is significant in many situations, including near threshold.

We search for the existence of the weakly bound He-He-Be molecules. The He-He-Be molecule is treated as a three-body system. By using hyperspherical coordinates, the Schr ouml;dinger equation for the triatomic system is solved in the adiabatic approximation. A bound state is found for each of the 3He-3He-9Be, 3He-4He-9Be, and 4He-4He- 9Be trimers, respectively.

a Stark decelerator, beams of neutral polar molecules can be accelerated, guided at a constant velocity, or decelerated. The effectiveness of this process is determined by the 6D volume in phase space from which molecules are accepted by the Stark decelerator. Couplings between the longitudinal and transverse motion of the molecules in the decelerator can reduce this acceptance. These couplings are nearly absent when the decelerator operates such that only every third electric field stage is used for deceleration, while extra transverse focusing is provided by the intermediate stages. For many applications, the acceptance of a Stark decelerator in this so-called s=3 mode significantly exceeds that of a decelerator in the conventionally used (s=1) mode. This has been experimentally verified by passing a beam of OH radicals through a 2.6 meter long Stark decelerator. The experiments are in quantitative agreement with the results of trajectory calculations, and can qualitatively be explained with a simple model for the 6D acceptance. These results imply that the 6D acceptance of a Stark decelerator in the s=3 mode of operation approaches the optimum value, i.e. the value that is obtained when any couplings are neglected.

We evaluate photoelectron angular anisotropy b-parameters for the process of sequential two-photon double electron ionization of helium within the lowest order time-independent perturbation theory. Our results indicate that for the photoelectron energies outside the interval (Eslow,Efast), where Eslow=w-IPHe+ and Efast=w-IPHe , there is a considerable deviation from the dipole angular distribution thus indicating the effect of electron correlation.

We study, both analytically and numerically, the formation and propagation of dark solitons in a superfluid Fermi gas in the crossover from Bardeen-Cooper-Schrieffer (BCS) superfluid to a Bose-Einstein condensate (BEC). Starting from a superfluid order-parameter equation we derive a Korteweg-de Vries equation for weak nonlinear excitations under quasi-one-dimensional and long wavelength approximations. We present dark soliton solutions valid for both BCS and BEC limits and also for the crossover, and show that dark solitons in different superfluid regimes possess different features. Particularly, a dark soliton in the BCS (BEC) regime has larger (smaller) propagating velocity and smaller (larger) spatial width. Upon moving to the boundary of the condensate, it generally decelerates and generates small radiations, which display different behavior in different superfluid regimes. We study also a head-on collision between two dark solitons and demonstrate that the phase shift due to the collision changes non-monotonically along the BCS-BEC crossover. All analytical results are checked by numerical simulations and good agreements between them are found.

The low lying excitations of coreless vortex states in F = 1 spinor Bose-Einstein condensates (BECs) are theoretically investigated using the Gross-Pitaevskii and Bogoliubov-de Gennes equations. The spectra of the elementary excitations are calculated for different spin-spin interaction parameters and ratios of the number of particles in each sublevel. There exist dynamical instabilities of the vortex state which are suppressed by ferromagnetic interactions, and conversely, enhanced by antiferromagnetic interactions. In both of the spin-spin interaction regimes, we find vortex splitting instabilities in analogy with scalar BECs. In addition, a phase separating instability is found in the antiferromagnetic regime.

We present a theoretical study of vortices within a harmonically trapped Bose-Einstein condensate in a rotating optical lattice. We find that proximity to the Mott insulating state dramatically affects the vortex structures. To illustrate we give examples in which the vortices: (i) all sit at a fixed distance from the center of the trap, forming a ring, or (ii) coalesce at the center of the trap, forming a giant vortex. We also model time-of-flight expansion.

We report the realization of quantum degenerate mixed gases of ytterbium (Yb) isotopes using all-optical methods. We have succeeded in cooling attractively interacting 176Yb atoms via sympathetic cooling down to below the Bose-Einstein transition temperature, coexisting with a stable condensate of 174Yb atoms with a repulsive interaction. We have observed a rapid atom loss in 176Yb atoms after cooling down below the transition temperature, which indicates the collapse of a 176Yb condensate. The sympathetic cooling technique has been applied to cool a 173Yb-174Yb Fermi-Bose mixture to the quantum degenerate regime.

We investigate decoherence in atom interferometry due to scattering from a background gas and show that the supposition that residual coherence is due to near forward scattering is incorrect. In fact, the coherent part is completely unscattered, though it is phase shifted. This recoil free process leaves both the atom and the gas in an unchanged state, but allows for the acquisition of a phase shift. This is essential to understanding decoherence in a separated arm atom interferometer, where a gas of atoms forms a refractive medium for a matter wave. Our work elucidates the actual microscopic, many-body, quantum mechanical scattering mechanism that gives rise to prior phenomenological results for the phase shift and decoherence.

Our recent work has demonstrated the superradiant writing and reading of collective coherence in a Bose-Einstein condensate [Phys. Rev. Lett. 99, 220407 (2007)]. Here we report the drastic improvement of the storage time realized by loading the atoms into an optical dipole trap, wherein unfavorable spin-dependent phase shift and spatial diffusion of atoms can be suppressed. The measured storage time was 0.57(2) ms, which is limited by temporal variation of atomic momentum due to harmonic oscillation in the trap.

Quantum interferometers are generally set so that phase differences between paths in coordinate space combine constructive or destructively. Indeed, the interfering paths can also meet in momentum space leading to momentum-space fringes. We propose and analyze a method to produce interference in momentum space by phase-imprinting part of a trapped atomic cloud with a detuned laser. For one-particle wave functions analytical expressions are found for the fringe width and shift versus the phase imprinted. The effects of unsharpness or displacement of the phase jump are also studied, as well as many-body effects, to determine the potential applicability of momentum-space interferometry. For a broad range of parameters and conditions it is found that a "dark notch" in the momentum distribution depends linearly on the phase imprinted, with maximal sensitivity for non-interacting atoms in the ground state of tight traps.

Recent progress in the field of ultracold gases has allowed the creation of phase-segregated Bose-Fermi systems. We present a theoretical study of their collective excitations at zero temperature. As the fraction of fermion to boson particle number increases, the collective mode frequencies take values between those for a fully bosonic and those for a fully fermionic cloud, with damping in the intermediate region. This damping is caused by fermions which are resonantly driven at the interface.

In a recent experiment [PRL 100, 040404 (2008)] an analog of photon-assisted tunneling has been observed for a Bose-Einstein condensate in an optical lattice subject to a constant force plus a sinusoidal shaking. Contrary to previous theoretical predictions, the width of the condensate was measured to be proportional to the square of the effective tunneling matrix element, rather than a linear dependence. For a simple model of two interacting bosons in a one-dimensional optical lattice, both analytical and numerical calculations indicate that such a transition from a linear to a quadratic dependence can be interpreted through the ballistic transport and the corresponding exact dispersion relation of bound boson pairs.

There exist two popular energy-momentum tensors for an electromagnetic wave in a dielectric medium. The Abraham expression is robust to experimental verification but more mathematically demanding, while the Minkowski expression is the foundation of a number of simplifications commonly found within the literature, including the relative refractive index transformation often used in modelling optical tweezers. These simplifications are based on neglecting the Minkowski tensor's material counterpart, a process known to be incompatible with conservation of angular momentum, and in conflict with experimental results, yet they are very successful in a wide range of circumstances. This paper combines existing constraints on their usage with recent theoretical analysis to obtain a list of conditions which much be satisfied to safely use the simplified Minkowski approach. Applying these conditions to an experiment proposed by Padgett et al., we find their prediction in agreement with that obtained using the total energy-momentum tensor.