Management of solitons in media with competing quadratic and cubic nonlinearities is investigated. Two schemes, using rapid modulations of a mismatch parameter, and of the Kerr nonlinearity parameter are studied. For both cases, the averaged in time wave equations are derived. In the case of mismatch management, the region of the parameters where stabilization is possible is found. In the case of Kerr nonlinearity management, it is shown that the effective chi(2) nonlinearity depends on the intensity imbalance between fundamental (FH) and second (SH) harmonics. Predictions obtained from the averaged equations are confirmed by numerical simulations of the full PDE’s.
The evolution of vector solitons under nonlinearity management is studied. The averaged over strong and rapid modulations in time of the inter-species interactions vector Gross-Pitaevskii equation (GPE) is derived. The averaging gives the appearance of the effective nonlinear quantum pressure depending on the population of the other component. Using this system of equations, the existence and stability of the vector solitons under the action of the strong nonlinearity management (NM) is investigated. Using a variational approach the parameters of NM vector solitons are found. The numerical simulations of the full time-dependent coupled GPE confirms the theoretical predictions.
Dynamics of matter waves in the atomic to molecular condensate transition with a time modulated atomic scattering length is investigated. The conditions for dynamical suppression of association of atoms into the molecular field are obtained.
The Zeno effect is investigated for soliton type pulses in a nonlinear directional coupler with dissipation. The effect consists in increase of the coupler transparency with increase of the dissipative losses in one of the arms. It is shown that localized dissipation can lead to switching of solitons between the arms. Power losses accompanying the switching can be fully compensated by using a combination of dissipative and active (in particular, parity-time-symmetric) segments.
The generation of Faraday waves in superfluid Fermi-Bose mixtures in elongated traps is investigated. The generation of waves is achieved by periodically changing a parameter of the system in time. Two types of modulations of parameters are considered: a variation of the fermion-boson scattering length and the boson-boson scattering length. We predict the properties of the generated Faraday patterns and study the parameter regions where they can be excited.
Collective oscillations of superfluid mixtures of ultra cold fermionic and bosonic atoms are investigated while varying the fermion-boson scattering length. We study the dynamics with respect to excited center of mass modes and breathing modes in the mixture. Parametric resonances are also analyzed when the scattering length varies periodically in time, by comparing partial differential equation (PDE) models and ordinary differential equation (ODE) models for the dynamics. An application to the recent experiment with fermionic Li-6 and bosonic Li-7 atoms, which approximately have the same masses, is discussed.
The dynamics of matter waves in the atomic to molecular condensate transition with a time-modulated atomic scattering length is investigated. Both the cases of rapid and slow modulations are studied. In the case of rapid modulations, the average over oscillations for the system is derived. The corresponding conditions for dynamical suppression of the association of atoms into the molecular field, or of second-harmonic generation in nonlinear optical systems, are obtained. For the case of slow modulations, we find resonant enhancement in the molecular field. We then illustrate chaos in the atomic-molecular BEC system. We suggest a sequential application of the two types of modulations, slow and rapid, when producing molecules.
Plasmonic gold nanorods are prime candidates for a variety of biomedical, spectroscopy, data storage, and sensing applications. It was recently shown that gold nanorods optically trapped by a focused circularly polarized laser beam can function as extremely efficient nanoscopic rotary motors. The system holds promise for-applications ranging from nanofluidic flow control and nanorobotics to biomolecular actuation and analysis. However, to fully exploit this potential, one needs to be able to control and understand heating effects associated with laser trapping. We investigated photothermal heating of individual rotating gold nanorods by simultaneously probing their localized surface plasmon resonance spectrum and rotational Brownian dynamics over extended periods of time. The data reveal an extremely slow nanoparticle reshaping process, involving migration of the order of a few hundred atoms per minute, for moderate laser powers and a trapping wavelength close to plasmon resonance. The plasmon spectroscopy and Brownian analysis allows for separate temperature estimates based on the refractive index and the viscosity of the water surrounding a trapped nanorod. We show that both measurements yield similar effective temperatures, which correspond to the actual temperature at a distance of the order 10-15 nm from the particle surface. Our results shed light on photothermal processes on the nanoscale and will be useful in evaluating the applicability and performance of nanorod motors and optically heated nanoparticles for a variety of applications.
This paper discusses the possibility of evaluating the shape of a free-form object in comparison with its shape prescribed by a CAD model. Measurements are made based on a single-shot recording using dual-wavelength holography with a synthetic wavelength of 1.4 mm. Each hologram is numerically propagated to different focus planes and correlated. The result is a vector field of speckle displacements that is linearly dependent on the local distance between the measured surface and the focus plane. From these speckle displacements, a gradient field of the measured surface is extracted through a proportional relationship. The gradient field obtained from the measurement is then aligned to the shape of the CAD model using the iterative closest point (ICP) algorithm and regularization. Deviations between the measured shape and the CAD model are found from the phase difference field, giving a high precision shape evaluation. The phase differences and the CAD model are also used to find a representation of the measured shape. The standard deviation of the measured shape relative the CAD model varies between 7 and 19 μm, depending on the slope.
The aim of this work is to evaluate the shape of a free form object using single shot digital holography. The digital holography results in a gradient field and wrapped phase maps representing the shape of the object. The task is then to find a surface representation from this data which is an inverse problem. To solve this inverse problem we are using regularization with additional shape information from the CAD-model of the measured object.
We review phase-space simulation techniques for fermions, showing how a Gaussian operator basis leads to exact calculations of the evolution of a many-body quantum system in both real and imaginary time. We apply such techniques to the Hubbard model and to the problem of molecular dissociation of bosonic molecules into pairs of fermionic atoms.
We present new approaches for solving constrained multicomponent nonlinear Schrödinger equations in arbitrary dimensions. The idea is to introduce an artificial time and solve an extended damped second order dynamic system whose stationary solution is the solution to the time-independent nonlinear Schrödinger equation. Constraints are often considered by projection onto the constraint set, here we include them explicitly into the dynamical system. We show the applicability and efficiency of the methods on examples of relevance in modern physics applications.
Gold nanorods can be optically trapped in aqueous solution and forced to rotate at kilohertz rates by circularly polarized laser light. This enables detailed investigations of local environmental parameters and processes, such as medium viscosity and nanoparticle-molecule reactions. Future applications may include nanoactuation and single-cell analysis. However, the influence of photothermal heating on the nanoparticle dynamics needs to be better understood in order to realize widespread and quantitative use. Here we analyze the hot Brownian motion of a rotating gold nanorod trapped in two dimensions by an optical tweezers using experiments and stochastic simulations. We show that, for typical settings, the effective rotational and translational Brownian temperatures are drastically different, being closer to the nanorod surface temperature and ambient temperature, respectively. Further, we show that translational dynamics can have a non-negligible influence on the rotational fluctuations due to the small size of a nanorod in comparison to the focal spot. These results are crucial for the development of gold nanorods into generic and quantitative optomechanical sensor and actuator elements. (C) 2017 Optical Society of America
We consider small systems of bosonic atoms rotating in a toroidal trap. Using the method of exact numerical diagonalization of the many-body Hamiltonian, we examine the transition from the Bose-Einstein condensed state to the Tonks-Girardeau state. The system supports persistent currents in a wide range between the two limits, even in the absence of Bose-Einstein condensation.
We present a digital holographic method to increase height range measurement with a reduced phase ambiguity using a dual-directional illumination. Small changes in the angle of incident illumination introduce phase differences between the recorded complex fields. We decrease relative phase difference between the recorded complex fields 279 and 139 times by changing the angle of incident 0.5° and 1°, respectively. A two cent Euro coin edge groove is used to measure the shape. The groove depth is measured as ≈300 . Further, numerical refocusing and analysis of speckle displacements in two different planes are used to measure the depth without a use of phase unwrapping process.
This paper describes a method to obtain an estimated digital reference wave from a single off-axis digital hologram that matches the actual experimental reference wave as closely as possible. The proposed method is independent of a reference flat plate and speckles. The digital reference wave parameters are estimated directly from the recorded phase information. The parameters include both the off-axis tilt angle and the curvature of the reference wave. Phase derivatives are used to extract the digital reference wave parameters without the need for a phase unwrapping process. Thus, problems associated with phase wrapping are avoided. Experimental results for the proposed method are provided. The simulated effect of the digital reference wave parameters on the reconstructed image phase distribution is shown. The pseudo phase gradient originating from incorrect estimation of the digital reference wave parameters and its effect on object reconstruction are discussed.
In this paper a single-shot digital holographic set-up with two orthogonally polarized reference beams is proposed to achieve rapid acquisition of Magneto-Optical Kerr Effect images. Principles of the method and the background theory for dynamic state of polarization measurement by use of digital holography are presented. This system has no mechanically moving elements or active elements for polarization control and modulation. An object beam is combined with two reference beams at different off-axis angles and is guided to a detector. Then two complex fields (interference terms) representing two orthogonal polarizations are recorded in a single frame simultaneously. Thereafter the complex fields are numerically reconstructed and carrier frequency calibration is done to remove aberrations introduced in multiplexed digital holographic recordings. From the numerical values of amplitude and phase, a real time quantitative analysis of the polarization state is possible by use of Jones vectors. The technique is demonstrated on a magnetic sample that is a lithographically patterned magnetic microstructure consisting of thin permalloy parallel stripes.
In an on line shape measurement in disturbed environment, use of many wavelengths in order to avoid phase ambiguity may become a problem as it is necessary to acquire all holograms simultaneously due to environmental disturbances. Therefore to make the shape data available the different holograms have to be extracted from a single recorded image in spectral domain. Appropriate cut areas in the Fourier method are therefore of great importance for decoding information carried by different wavelengths. Furthermore using different laser sources, induces aberration and pseudo phase changes which must be compensated. To insure any phase change is only because of the object shape, calibration is therefore indispensable. For this purpose, effects of uncontrolled carrier frequency filtering are discussed. A registration procedure is applied using minimum speckle displacements to find the best cut area to extract and match the interference terms. Both holograms are numerically propagated to a focus plane to avoid any unknown errors. Deviations between a reference known plate and its measurement are found and used for calibration. We demonstrate that phase maps and speckle displacements can be recovered free of chromatic aberrations. To our knowledge, this is the first time that a single shot dual wavelength calibration is reported by defining a criteria to make the spatial filtering automatic avoiding the problems of manual methods. The procedure is shown to give shape accuracy of 35ÎŒm with negligible systematic errors using a synthetic wavelength of 1.1 mm.
The objective of this paper is to describe a fast and robust automatic single-shot dual-wavelength holographic calibration method that can be used for online shape measurement applications. We present a model of the correction in two terms for each lobe, one to compensate the systematic errors caused by off-axis angles and the other for the curvature of the reference waves, respectively. Each hologram is calibrated independently without a need for an iterative procedure or information of the experimental set-up. The calibration parameters are extracted directly from speckle displacements between different reconstruction planes. The parameters can be defined as any fraction of a pixel to avoid the effect of quantization. Using the speckle displacements, problems associated with phase wrapping is avoided. The procedure is shown to give a shape accuracy of 34 μm using a synthetic wavelength of 1.1 mm for a measurement on a cylindrical test object with a trace over a field of view of 18  mm×18  mm.
We present a calibration method which allows single shot dual wavelength online shape measurement in a disturbed environment. Effects of uncontrolled carrier frequency filtering are discussed as well. We demonstrate that phase maps and speckle displacements can be recovered free of chromatic aberrations. To our knowledge, this is the first time that a single shot dual wavelength calibration is reported by defining a criteria to make the spatial filtering automatic avoiding the problems of manual methods. The procedure is shown to give shape accuracy of 35Â Âµm with negligible systematic errors using a synthetic wavelength of 1.1Â mm.
A new method to measure shape by analyzing the speckle movements in images generated by numerical propagation from dual-wavelength holograms is presented. The relationship of the speckle movements at different focal distances is formulated, and it is shown how this carries information about the surface position as well as the local slope of the object. It is experimentally verified that dual-wavelength holography and numerically generated speckle images can be used together with digital speckle correlation to retrieve the object shape. From a measurement on a cylindrical test object, the method is demonstrated to have a random error in the order of a few micrometers.
A new technique to measure depth based on dual wavelength digital holography and image correlation of speckle movements is demonstrated. By numerical refocusing of the complex optical field to different focus planes and by measuring the speckle movements caused by a wavelength shift both the object surface position and its local slope can be determined. It is shown how the speckle movement varies linearly with the surface slope, the wavelength shift and the distance of the numerical propagation. This gives a possibility to measure the slope with approximately the same precision as from the interferometric phase maps. In addition, when the object surface is in focus there is no speckle movement so by estimating in what plane the speckle movement is zero the absolute surface position can be measured.
High speed photography of a reverse impact scenario was taken in order to make shape measurement. The results from the shape measurements were then compared with results from numerical simulations in order to evaluate the possibility to use noncontact shape measurement as a validation tool in future simulations.
We present a dual-directional illumination digital holographic method to increase height range measurement with a reduced phase ambiguity. Small change in the illumination angle of incident introduce phase difference between the recorded complex fields. We decrease relative phase difference between the recorded complex field 279 and 139 times by changing the angle of incident 0.5° and 1°, respectively. A two cent Euro coin edge groove is used to measure the shape. The groove depth is measured as ≈ 300μm. Further, numerical re-focusing and analysis of speckle displacements in two different planes are used to measure the depth without a use of phase unwrapping process.
Nanoparticles made of high index dielectric materials have seen a surge of interest and have been proposed for various applications, such as metalenses, light harvesting and directional scattering. With the advent of fabrication techniques enabling colloidal suspensions, the prospects of optical manipulation of such nanoparticles becomes paramount. High index nanoparticles support electric and magnetic multipolar responses in the visible regime and interference between such modes can give rise to highly directional scattering, in particular a cancellation of back-scattered radiation at the first Kerker condition. Here we present a study of the optical forces on silicon nanoparticles in the visible and near infrared calculated using the transfer matrix method. The zero-backscattering Kerker condition is investigated as an avenue to reduce radiation pressure in an optical trap. We find that while asymmetric scattering does reduce the radiation pressure, the main determining factor of trap stability is the increased particle response near the geometric resonances. The trap stability for non-spherical silicon nanoparticles is also investigated and we find that ellipsoidal deformation of spheres enables trapping of slightly larger particles.
Optically trapped nanoparticles can be used as efficient mobile probes of nanoscopic forces and temperatures. However, it is crucial that the trapped particle has minimal influence on the system under study while providing a strong enough optical response to actually allow for optical manipulation. This puts severe constraints on the particle size and thermal properties. In particular, strong optical responses associated with plasmon resonances in noble metal nanoparticles and Mie resonances in high index dielectric particles can significantly affect trap stability through enhanced radiation pressure forces and photoinduced heating. Using Mie theory and hot Brownian motion analysis, we calculate trap stability and photothermal properties for nanospheres composed of the best (Ag) and most widely used (Au) plasmonic materials as well as for crystalline and amorphous Si, the prototypic high-index dielectric, using polystyrene as a low-index reference material. We calculate trap stability properties for optical tweezers based on high numerical aperture optics (NA = 1.2) for three of the most widely used laser wavelengths (532, 785, and 1064 nm) and for the case of trapping in water. The results reveal the specific particle size ranges for which optical tweezing is possible in two and three dimensions and indicate that crystalline Si nanoparticles trapped using near-infrared laser beams are the optimal choice for temperature-sensitive optical manipulation applications with small particles.
Autosomal recessive retinal degenerative diseases cause visual impairment and blindness in both humans and dogs. Currently, no standard treatment is available, but pioneering gene therapy-based canine models have been instrumental for clinical trials in humans. To study a novel form of retinal degeneration in Labrador retriever dogs with clinical signs indicating cone and rod degeneration, we used whole-genome sequencing of an affected sib-pair and their unaffected parents. A frameshift insertion in the ATP binding cassette subfamily A member 4 (ABCA4) gene (c.4176insC), leading to a premature stop codon in exon 28 (p.F1393Lfs*1395), was identified. In contrast to unaffected dogs, no full-length ABCA4 protein was detected in the retina of an affected dog. The ABCA4 gene encodes a membrane transporter protein localized in the outer segments of rod and cone photoreceptors. In humans, the ABCA4 gene is associated with Stargardt disease (STGD), an autosomal recessive retinal degeneration leading to central visual impairment. A hallmark of STGD is the accumulation of lipofuscin deposits in the retinal pigment epithelium (RPE). The discovery of a canine homozygous ABCA4 loss-of-function mutation may advance the development of dog as a large animal model for human STGD.
We consider a “symmetric” quantum droplet in two spatial dimensions, which rotates in a harmonic potential, focusing mostly on the limit of “rapid” rotation. We examine this problem using a purely numerical approach, as well as a semianalytic Wigner-Seitz approximation (first developed by Baym, Pethick, and their co-workers) for the description of the state with a vortex lattice. Within this approximation we assume that each vortex occupies a cylindrical cell, with the vortex-core size treated as a variational parameter. Working with a fixed angular momentum, as the angular momentum increases and depending on the atom number, the droplet accommodates none, few, or many vortices, before it turns to center-of-mass excitation. For the case of a “large” droplet, working with a fixed rotational frequency of the trap Ω, as Ω approaches the trap frequency 𝜔, a vortex lattice forms, the number of vortices increases, the mean spacing between them decreases, while the “size” of each vortex increases as compared to the size of each cell. In contrast to the well-known problem of contact interactions, where we have melting of the vortex lattice and highly correlated many-body states, here no melting of the vortex lattice is present, even when Ω=𝜔. This difference is due to the fact that the droplet is self-bound. For Ω=𝜔, the “smoothed” density distribution becomes a flat top, very much like the static unconfined droplet. When Ω exceeds 𝜔, the droplet maintains its shape and escapes to infinity, via center-of-mass motion.
We investigate the rotational properties of a two-component, two-dimensional self-bound quantum droplet, which is confined in a harmonic potential and compare them with the well-known problem of a single-component atomic gas with contact interactions. For a fixed value of the trap frequency, choosing some representative values of the atom number, we determine the lowest-energy state, as the angular momentum increases. For a sufficiently small number of atoms, the angular momentum is carried via center-of-mass excitation. For larger values, when the angular momentum is sufficiently small, we observe vortex excitation instead. Depending on the actual atom number, one or more vortices enter the droplet. Beyond some critical value of the angular momentum, however, the droplet does not accommodate more vortices and the additional angular momentum is carried via center-of-mass excitation in a "mixed" state. Finally, the excitation spectrum is also briefly discussed.
We investigate the rotational properties of quantum droplets, which form in a mixture of two Bose-Einstein condensates, in the presence of an anharmonic trapping potential. We identify various phases as the atom number and the angular momentum or angular velocity of the trap vary. These phases include center-of-mass–like excitation (without or with vortices), vortices of single and multiple quantization, etc. Finally, we compare our results with those of the single-component problem.
Currently used analytical techniques for halogenated aromatic environmental contaminants such as polychlorinated dibenzo-p-dioxins (PCDDs), dibenzofurans (PCDFs), and biphenyls (PCBs), also known as legacy persistent organic pollutants, are based on gas chromatographic separation of target analytes and detection by mass spectrometry. The coupling of packed column supercritical fluid chromatography (SFC) to atmospheric pressure ionization mass spectrometry (API/MS) could allow for the concurrent analysis of thermally labile and legacy halogenated environmental contaminants if ionization can be sufficiently optimized. The evaluation of positive ion atmospheric pressure chemical ionization (APCI) and atmospheric pressure photoionization (APPI) as well as possible charge transfer dopants for the generation of molecular ion isotopomeric clusters of halogenated environmental contaminants with minimal fragmentation has been completed. Using the investigated parameters, positive ion APPI was found to be the more sensitive technique. Of the aromatic and cycloalkane dopants investigated, only fluorobenzene and trifluorotoluene were found to be effective dopants for the halogenated aromatic target analytes (PCDDs, PCDFs, and PCBs). Experiments involving deuterated dopants confirmed that reactive species generated by cycloalkanes were quenched by the SFC eluent rendering them unusable in conjunction with the investigated separation technique. Alternatively, aromatic dopants were found to be less susceptible to quenching by the SFC eluent and fluorobenzene was determined to be the most effective charge transfer dopant for PCDDs, PCDFs, and PCBs. To demonstrate the applicability of the optimized ionization conditions, SFC-API/MS has been used for the concurrent analysis of legacy halogenated aromatic environmental contaminants (PCDDs, PCDFs, and PCBs) and thermally labile analytes (alpha, beta, and gamma isomers of hexabromocyclododecane).
We study the rotational properties of a two-component Bose-Einstein condensed gas of distinguishable atoms which are confined in a ring potential using both the mean-field approximation, as well as the method of diagonalization of the many-body Hamiltonian. We demonstrate that the angular momentum may be given to the system either via single-particle, or "collective" excitation. Furthermore, despite the complexity of this problem, under rather typical conditions the dispersion relation takes a remarkably simple and regular form. Finally, we argue that under certain conditions the dispersion relation is determined via collective excitation. The corresponding many-body state, which, in addition to the interaction energy minimizes also the kinetic energy, is dictated by elementary number theory.
In this paper, we present a tailored multiwavelength Yb-fiber laser source in the 1.03 μm spectral region for spatially multiplexed digital holographic acquisitions. The wavelengths with bandwidths below 0.1 nm were spectrally separated by approximately 1 nm by employing fiber Bragg gratings for spectral control. As a proof of concept, the shape of a cylindrically shaped object with a diameter of 48 mm was measured. The holographic acquisition was performed in single-shot dual-wavelength mode with a synthetic wavelength of 1.1 mm, and the accuracy was estimated to be 3% of the synthetic wavelength.
We show that a dilute harmonically trapped two-component gas of fermionic atoms with a weak repulsive interaction has a pronounced super-shell structure: The shell fillings due to the spherical harmonic trapping potential are modulated by a beat mode. This changes the "magic numbers" occurring between the beat nodes by half a period. The length and amplitude of this beating mode depend on the strength of the interaction. We give a simple interpretation of the beat structure in terms of a semiclassical trace formula for the symmetry breaking U(3)→SO(3).
We studied scattering and extinction of individual silver nanorods coupled to the J-aggregate form of the cyanine dye TDBC as a function of plasmon - exciton detuning. The measured single particle spectra exhibited a strongly suppressed scattering and extinction rate at wavelengths corresponding to the J-aggregate absorption band, signaling strong interaction between the localized surface plasmon of the metal core and the exciton of the surrounding molecular shell. In the context of strong coupling theory, the observed "transparency dips" correspond to an average vacuum Rabi splitting of the order of 100 meV, which approaches the plasmon dephasing rate and, thereby, the strong coupling limit for the smallest investigated particles. These findings could pave the way towards ultra-strong light-matter interaction on the nanoscale and active plasmonic devices operating at room temperature.
We consider the existence and stability of solitons in a 𝜒(2) coupler. Both the fundamental and second harmonics (SHs) undergo gain in one of the coupler cores and are absorbed in the other one. The gain and loss are balanced, creating a parity-time (𝒫𝒯) symmetric configuration. We present two types of families of 𝒫𝒯-symmetric solitons having equal and different profiles of the fundamental and SHs. It is shown that the gain and loss can stabilize solitons. The interaction of stable solitons is shown. In the cascading limit, the model is reduced to the 𝒫𝒯-symmetric coupler with effective Kerr-type nonlinearity and the balanced nonlinear gain and loss.
We consider a Bose-Einstein condensate, which is confined ina very tight toroidal/annular trap,in the presence of a potential, which breaks the axial symmetry of the Hamiltonian. We investigate the stationary states of the condensate, when its density distribution co-rotates with the symmetry-breaking potential. As the strength of the potential increases, we have a gradual transition from vortex excitation to solid-body-like motion. Of particular importance are states where the system is static and yet it has a nonzero current/circulation, which is a realization of persistentcurrents/reflectionless potentials.
We calculate level densities and pairing gaps for an ultracold dilute gas of fermionic atoms in harmonic traps under the influence of mean field and anharmonic quartic trap potentials. Supershell nodes, which were found in Hartree-Fock calculations, are calculated analytically within periodic orbit theory as well as from WKB calculations. For attractive interactions, the underlying level densities are crucial for pairing and supershell structures in gaps are predicted.
We examine bosonic atoms that are confined in a toroidal, quasi-one-dimensional trap, subjected to a random potential. The resulting inhomogeneous atomic density is smoothened for sufficiently strong, repulsive interatomic interactions. Statistical analysis of our simulations show that the gas supports persistent currents, which become more fragile due to the disorder.
Motivated by recent experiments in Bose-Einstein condensed atoms that have been confined in toroidal traps, we examine the stability of persistent currents in such systems. We investigate the extent that the stability of these currents may be tunable, and the possible difficulties in their creation and detection.
We examine the propagation of solitary waves in elongated clouds of trapped bosonic atoms as the confinement, the strength of the interatomic interaction, and the atom density are varied. We identify three different physical regimes and develop a general formalism that allows us to interpolate between them. Finally we pay special attention to the transition to the Tonks-Girardeau limit of strongly interacting bosons.
We consider a mixture of a Bose-Einstein condensate, with a paired Fermi superfluid, confined in a ring potential. We start with the ground state of the two clouds, identifying the boundary between the regimes of their phase separation and phase coexistence. We then turn to the rotational response of the system. In the phase-separated regime, we have center of mass excitation. When the two species coexist, the spectrum has a rich structure, consisting of continuous and discontinuous phase transitions. Furthermore, for a reasonably large population imbalance it develops a clear quasi- periodic behaviour, in addition to the one due to the periodic boundary conditions. It is then favourable for the one component to reside in a plane-wave state, with a homogeneous density distribution, and the problem resembles that of a single-component system.
We study atom-atom correlations and relative number squeezing in the dissociation of a Bose-Einstein condensate (BEC) of molecular dimers made of either bosonic or fermionic atom pairs. Our treatment addresses the role of the spatial inhomogeneity of the molecular BEC on the strength of correlations in the short time limit. We obtain explicit analytic results for the density-density correlation functions in momentum space, and show that the correlation widths and the degree of relative number squeezing are determined merely by the shape of the molecular condensate.
We analyze atom-atom correlations in the s -wave scattering halo of two colliding condensates. By developing a simple perturbative approach, we obtain explicit analytic results for the collinear (CL) and back-to-back (BB) correlations corresponding to realistic density profiles of the colliding condensates with interactions. The results in the short-time limit are in agreement with the first-principles simulations using the positive- P representation and provide analytic insights into the experimental observations of Perrin [Phys. Rev. Lett. 99, 150405 (2007)]. For long collision durations, we predict that the BB correlation becomes broader than the CL correlation.
We theoretically analyze dissociation of a harmonically trapped Bose-Einstein condensate of molecular dimers and examine how the spatial inhomogeneity of the molecular condensate affects the conversion dynamics and the atom-atom pair correlations in the short-time limit. Both fermionic and bosonic statistics of the constituent atoms are considered. Using the undepleted molecular-field approximation, we obtain explicit analytic results for the asymptotic behavior of the second-order correlation functions and for the relative number squeezing between the dissociated atoms in one, two, and three spatial dimensions. Comparison with the numerical results shows that the analytic approach employed here captures the main underlying physics and provides useful insights into the dynamics of dissociation for conversion efficiencies up to 10%. The results show explicitly how the strength of atom-atom correlations and relative number squeezing degrade with the reduction of the size of the molecular condensate.
We demonstrate that the quantum dynamics of a many-body Fermi-Bose system can be simulated using a Gaussian phase-space representation method. In particular, we consider the application of the mixed fermion-boson model to ultracold quantum gases and simulate the dynamics of dissociation of a Bose-Einstein condensate of bosonic dimers into pairs of fermionic atoms. We quantify deviations of atom-atom pair correlations from Wick's factorization scheme, and show that atom-molecule and molecule-molecule correlations grow with time, in clear departures from pairing mean-field theories. As a first-principles approach, the method provides benchmarking of approximate approaches and can be used to validate dynamical probes for characterizing strongly correlated phases of fermionic systems.
A Gaussian operator basis provides a means to formulate phase-space simulations of the real- and imaginary-time evolution of quantum systems. Such simulations are guaranteed to be exact while the underlying distribution remains well-bounded, which defines a useful simulation time. We analyse the application of the Gaussian phase-space representation to the dynamics of the dissociation of an ultra-cold molecular gas. We show how the choice of mapping to stochastic differential equations can be used to tailor the stochastic behaviour, and thus the useful simulation time. In the phase-space approach, it is only averages of stochastic trajectories that have a direct physical meaning. Whether particular constants of the motion are satisfied by individual trajectories depends on the choice of mapping, as we show in examples.
We examine the spin asymmetry of ground states for two-dimensional, harmonically trapped two-component gases of fermionic atoms at zero temperature with weakly repulsive short-range interactions. Our main result is that, in contrast to the three-dimensional case, in two dimensions a non-trivial spin-asymmetric phase can only be caused by the shell structure. A simple, qualitative description is given in terms of an approximate single-particle model, comparing well to the standard results of Hartree-Fock or direct diagonalization methods.