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Motivated by the recent experimental realization of ultracold quantum gases in shell topology, we propose a straightforward implementation of matter-wave lensing techniques for shell-shaped Bose–Einstein condensates. This approach allows to significantly extend the free evolution time of the condensate shell after release from the trap and enables the study of novel quantum many-body effects on curved geometries. With both analytical and numerical methods we derive optimal parameters for realistic schemes to conserve the shell shape of the condensate for times up to hundreds of milliseconds.

The study of molecular physics using ultracold gases has provided a unique probe into the fundamental properties of nature and offers new tools for quantum technologies. In this article we outline how ultracold molecular physics in a space environment opens opportunities for (a) exploring ultra-low energy regimes of molecular physics with high efficiency, (b) providing a toolbox of capabilities for fundamental physics, and (c) enabling new classes of matter-wave interferometers with applications in precision measurement for fundamental and many-body physics.

Progress in understanding quantum systems has been driven by the exploration of the geometry, topology, and dimensionality of ultracold atomic systems. The NASA Cold Atom Laboratory (CAL) aboard the International Space Station has enabled the study of ultracold atomic bubbles, a terrestrially-inaccessible topology. Proof-of-principle bubble experiments have been performed on CAL with an rf-dressing technique; an alternate technique (dual-species interaction-driven bubbles) has also been proposed. Both techniques can drive discovery in the next decade of fundamental physics research in microgravity., 17 pages, 2 figures

Fifty years ago Kostin (J Chem Phys 57(9):3589–3591, 1972. https://doi.org/10.1063/1.1678812) proposed a description of damping in quantum mechanics based on a nonlinear Schrödinger equation with the potential being governed by the phase of the wave function. We show for the example of a moving Gaussian wave packet, that the deceleration predicted by this equation is the result of the same non-dissipative, homogeneous but time-dependent force, that also stops a classical particle. Moreover, we demonstrate that the Kostin equation is a special case of the linear Schrödinger equation with three potentials: (i) a linear potential corresponding to this stopping force, (ii) an appropriately time-dependent parabolic potential governed by a specific time dependence of the width of the Gaussian wave packet and (iii) a specific time-dependent off-set. The freedom of the width opens up the possibility of engineering the final state by the time dependence of the quadratic potential. In this way the Kostin equation is a precursor of the modern field of coherent control. Motivated by these insights, we analyze in position and in phase space the deceleration of a Gaussian wave packet due to potentials in the linear Schrödinger equation similar to those in the Kostin equation., publishedVersion

We investigate bright and dark diffractive focusing emerging in the free propagation of specific wave profiles. These general wave phenomena manifest themselves in matter, water, and classical waves. In this article, we lay the foundations for these effects and illustrate their origin in Wigner phase space. Our theoretical studies are supported by experimental demonstrations of dark focusing in water waves. Moreover, by using different phase slits we analyze several aspects of bright and dark focusing for classical and matter waves., publishedVersion

We show that in order to guide waves, it is sufficient to periodically truncate their edges. The modes supported by this type of wave guide propagate freely between the slits, and the propagation pattern repeats itself. We experimentally demonstrate this general wave phenomenon for two types of waves: (i) plasmonic waves propagating on a metal-air interface that are periodically blocked by nanometric metallic walls, and (ii) surface gravity water waves whose evolution is recorded, the packet is truncated, and generated again to show repeated patterns. This guiding concept is applicable for a wide variety of waves., 5 pages, 4 figures

We study phase contributions of wave functions that occur in the evolution of Gaussian surface gravity water wave packets with nonzero initial momenta propagating in the presence and absence of an effective external linear potential. Our approach takes advantage of the fact that in contrast to matter waves, water waves allow us to measure both their amplitudes and phases., 6 pages, 1 table, 2 figures. Accepted to EPJ-ST, not published yet

We provide an analytical proof of universality for bound states in one-dimensional systems of two and three particles, valid for short-range interactions with negative or vanishing integral over space. The proof is performed in the limit of weak pair-interactions and covers both binding energies and wave functions. Moreover, in this limit the results are formally shown to converge to the respective ones found in the case of the zero-range contact interaction.

We study the evolution of linear and nonlinear Talbot carpets emerging in surface gravity water waves. In our measurements, we are able to record both amplitude and phase of the Temporal Talbot effect.

We propose a straightforward implementation of the phenomenon of diffractive focusing with uniform atomic Bose-Einstein condensates. Both, analytical as well as numerical methods not only illustrate the influence of the atom-atom interaction on the focusing factor and the focus time, but also allow us to derive the optimal conditions for observing focusing of this type in the case of interacting matter waves., Comment: 26 pages, 7 figures

We study a heavy-heavy-light three-body system confined to one space dimension. Both binding energies and corresponding wave functions are obtained for (i) the zero-range, and (ii) two finite-range attractive heavy-light interaction potentials. In case of the zero-range potential, we apply the method of Skorniakov and Ter-Martirosian to explore the accuracy of the Born-Oppenheimer approach. For the finite-range potentials, we solve the Schr\"odinger equation numerically using a pseudospectral method. We demonstrate that when the two-body ground state energy approaches zero, the three-body bound states display a universal behavior, independent of the shape of the interaction potential., Comment: 16 pages, 9 figures, 1 table

We present a unique matter-wave interferometer whose phase scales with the cube of the time the atom spends in the interferometer. Our scheme is based on a full-loop Stern-Gerlach interferometer incorporating four magnetic field gradient pulses to create a state-dependent force. In contrast to typical atom interferometers which make use of laser light for the splitting and recombination of the wave packets, this realization uses no light and can therefore serve as a high-precision surface probe at very close distances., Comment: Phys. Rev. Lett., in print, https://journals.aps.org/prl/

In many experiments involving cold atoms, it is crucial to know the strength of the magnetic field and/or the magnetic field gradient at the precise location of a measurement. While auxiliary sensors can provide some of this information, the sensors are usually not perfectly co-located with the atoms and so can only provide an approximation to the magnetic field strength. In this article, we describe a technique to measure the magnetic field, based on Raman spectroscopy, using the same atomic fountain source that will be used in future magnetically sensitive measurements.

Quantum sensors based on matter-wave interferometry are promising candidates for high-precision gravimetry and inertial sensing in space. The favorable sources for the coherent matter waves in these devices are Bose–Einstein condensates. A reliable prediction of their dynamics, which is governed by the Gross–Pitaevskii equation, requires suitable analytical and numerical methods, which take into account the center-of-mass motion of the condensate, its rotation, and its spatial expansion by many orders of magnitude. In this chapter, we present an efficient way to study their dynamics in time-dependent rotating traps that meet this objective. Both an approximate analytical solution for condensates in the Thomas–Fermi regime and dedicated numerical simulations on a variable adapted grid are discussed. We contrast and relate our approach to previous alternative methods and provide further results, such as analytical expressions for the one- and two-dimensional spatial density distributions and the momentum distribution in the long-time limit that are of immediate interest to experimentalists working in this field of research.

The quantum mechanical propagator of a massive particle in a linear gravitational potential derived already in 1927 by Earle H. Kennard \cite{Kennard,Kennard2} contains a phase that scales with the third power of the time $T$ during which the particle experiences the corresponding force. Since in conventional atom interferometers the internal atomic states are all exposed to the same acceleration $a$, this $T^3$-phase cancels out and the interferometer phase scales as $T^2$. In contrast, by applying an external magnetic field we prepare two different accelerations $a_1$ and $a_2$ for two internal states of the atom, which translate themselves into two different cubic phases and the resulting interferometer phase scales as $T^3$. We present the theoretical background for, and summarize our progress towards experimentally realizing such a novel atom interferometer., Comment: submitted to the special issue of Applied Physics B

We analyze the spin dynamics of an out-of-equilibrium large spin dipolar atomic Bose gas in an optical lattice. We observe a smooth crossover from a complex oscillatory behavior to an exponential behavior throughout the Mott to superfluid transition. While both of these regimes are well described by our theoretical models, we provide data in the intermediate regime where dipolar interactions, contact interactions, and super-exchange mechanisms compete. In this strongly correlated regime, spin dynamics and transport are coupled, which challenges theoretical models for quantum magnetism., Comment: 8 pages, 5 figures, includes supplemental material

We discuss the physical sense and interpretation of the Maeda—Gallagher experiment (2004) in which the probability of ionisation of Rydberg Li atoms perturbed by the resonance microwave field by a short half-cycle pulse was measured. The periodic dependence of the ionisation probability wi on the delay time t0 of the half-cycle pulse with respect to the instant of switching on the microwave field is found. The oscillation period of the function wi(t0) is equal to the Kepler period of a Rydberg electron. It is shown that the interpretation of this experiment by the authors in terms of localised wave packets has no grounds and neglects basic processes proceeding in the microwave field. An alternative interpretation is proposed and, as the first step, the structure of the Rydberg wave function formed in the resonance microwave field is studied.

We investigate entanglement of electrons and positrons produced via absorption by a vacuum of two or several photons from two external electromagnetic waves. The waves are modelled by finite-length focused pulses. Structures of the arising electron and positron wave packets are investigated in the momentum and coordinate representations. Conditional and unconditional widths of these wave packets, as well as the Schmidt number K are found, and they are used to evaluate the degree of entanglement. The conditions are found when entanglement is large. It is shown that the highest entanglement can be reached at nonrelativistic energies of electrons and positrons. Possibilities of observing the entanglement effects in experiments on pair production are discussed.

Strong and/or short laser pulses provide one avenue for rapid separation of composite quantum systems. Daughter particles can exhibit subtle aspects of quantum entanglement. We show that a Gaussian approximation provides a unifying overview of rapidly separating systems in many contexts, and propose using combined single-particle and coincidence measurements of wave-packet widths of bipartite systems for experimental observation of the degree of entanglement.

The results on non-spreading Michelangelo wave packets [7,8] are generalized to the case of a semi-open two-level system when some fraction of atoms falls back to the lower state due to spontaneous transitions. The proposed approach is based on the solution of the Generalized Optical Bloch Equations for the atomic density matrix. The spatial features of arising non-spreading wave packets as well as the atomic momentum distribution are compared with the case of an open two-level system.

The formation of two-dimensional nonspreading atomic wave packets produced in the interaction of a beam of two-level atoms with two standing light waves polarised in the same plane is considered. The mechanism providing a dispersionless particle dynamics is the balance of two processes: a rapid decay of the atomic wave function away from the field nodes due to spontaneous transitions to nonresonance states and the quantum broadening of the wave packets formed in the close vicinity of field nodes. Coordinate-dependent amplitudes and phases of the two-dimensional wave packets were found for the j(g) = 0 j(c) = 1 transition.

The Kapitza-Dirac effect (KDE), or the scattering of electrons by a standing light wave, is considered quantum mechanically with electron states before scattering taken in the form of wavepackets with homogeneously distributed `centres of mass'. The angular distribution functions of electrons after scattering and the average angle of scattering are found. This approach is used to establish the applicability conditions of purely classical, purely quantum-mechanical and intermediate results in the theory of KDE, as well as to describe some new regimes of scattering, characteristics of which depend explicitly on the size of the wavepackets before scattering.

The scattering of electrons on a standing electromagnetic wave (the Kapitza-Dirac effect) is considered within the quantum-mechanical and classical descriptions of the motion of electrons. The mean scattering angle and the distribution function of the electrons after scattering are found. It is shown that assignment of the initial electronic wave function in the form of a plane wave in the quantum-mechanical picture gives rise to the characteristic parameter β=mc 2/ħω 2 τ (where ω and τ are the frequency of the field and the duration of the interaction), which separates the regions of Bragg (β≪1) and nearly classical (β ≫1) scattering. When β≫1, the mean scattering angle does not depend on the choice of the description method, but the distribution functions of the electrons after scattering in the quantum and classical approaches differ significantly. When β≪1, both the distribution function and the mean scattering angle differ. Modification of the quantum theory and assignment of the initial electronic wave function in the form of a more or less localized wave packet are apparently needed to eliminate the differences discovered. The results obtained can be used to determine the dimensions of the wave packet which characterizes the state of electrons in a beam from experiments on scattering from a standing light wave.

We employ the Born-Oppenheimer approximation to find the effective potential in a three-body system consisting of a light particle and two heavy ones when the heavy-light short-range interaction potential has a resonance corresponding to a non-zero orbital angular momentum. In the case of an exact resonance in the p-wave scattering amplitude, the effective potential is attractive and long-range, namely it decreases as the third power of the inter-atomic distance. Moreover, we show that the range and power of the potential, as well as the number of bound states are determined by the mass ratio of the particles and the parameters of the heavy-light short-range potential., 5 pages, submitted to Phys. Rev. Lett

We consider the scattering of an atom by a sequence of two near-resonant standing light waves each formed by two running waves with slightly different wave vectors. Due to opposite detunings of the two standing waves and within the rotating wave approximation, the adiabatic approximation applied to the atomic center-of-mass motion and a smooth turn-on and -off of the interaction, the dynamical phase cancels out and the final state of the atom differs from the initial one only by the sum of the two Berry phases accumulated in the two interaction regions. This phase depends on the position of the atom in a way such that the wave packet emerging from the scattering region will focus, which constitutes a novel method to observe the Berry phase without resorting to interferometric methods., 14 pages, 4 figures

We propose a lens for atoms with reduced chromatic aberrations and calculate its focal length and spot size. In our scheme a two-level atom interacts with a near-resonant standing light wave formed by two running waves of slightly different wave vectors, and a far-detuned running wave propagating perpendicular to the standing wave. We show that within the Raman-Nath approximation and for an adiabatically slow atom-light interaction, the phase acquired by the atom is independent of the incident atomic velocity., 5 pages, one figure

We analyse scattering of a heavy atom off a weakly bound molecule comprising an identical heavy and a light atom in the Born-Oppenheimer approximation. We focus on the situation where the heavy atoms are bosons, which was realized in several experiments. The elastic and inelastic cross sections for the atom-molecular scattering exhibit a series of resonances corresponding to three-body Efimov states. Resonances in elastic collisions are accessible experimentally through thermalization rates, and thus constitute an alternative way of observing Efimov states., 4 pages, 2 figures

We show that the wave packet of a biphoton generated via spontaneous parametric down-conversion is strongly anisotropic. Its anisotropic features manifest themselves very clearly in comparison with measurements performed in two different schemes: When the detector scanning plane is perpendicular or parallel to the plane containing the crystal optical axis and the laser axis. The first of these two schemes is traditional whereas the second one gives rise to such unexpected results, such as anomalously strong narrowing of the biphoton wave packet measured in the coincidence scheme and very high degree of entanglement. The results are predicted theoretically and confirmed experimentally.

Wave packet structure of biphoton states arising in the process of spontaneous parametric down-conversion (SPDC) is studied theoretically and experimentally, and its relation with entanglement is discussed. In theory, a new expression is found for the biphoton wave function, in which anisotropy of the crystal refractive index is properly taken into account. Under the conditions of the experiment we report, the anisotropy effects are shown to be very strong. A scheme, optimal for observing extremely narrow coincidence angular photon distributions is found to be that in which the plane containing both the laser axis and the optical axis of a crystal coincides with the observation plane. The opposite, commonly investigated, case is that when these two planes are orthogonal to each other. We show that in the optimal geometry the coincidence angular distribution can be almost 20 times narrower than in the traditional scheme of measurements, and about 10 times narrower than the pump. Narrowing of coincidence distributions in the optimal geometry is accompanied by broadening the single-particle distributions, and this broadening is stronger pronounced in the optimal than in the commonly used geometry. The ratio R of widths of the single-particle and coincidence distributions in the optimal geometry appears to be as large as about 100, and we interpret this as an appropriate evaluation of the degree of entanglement accumulated in biphoton states. The results described are obtained theoretically and perfectly confirmed experimentally.

We show that the wave packet of a biphoton generated via spontaneous parametric down conversion is strongly anisotropic. Its anisotropic features manifest themselves very clearly in comparison of measurements performed in two different schemes: when the detector scanning plane is perpendicular or parallel to the plane containing the crystal optical axis and the laser axis. The first of these two schemes is traditional whereas the second one gives rise to such unexpected new results as anomalously strong narrowing of the biphoton wave packet measured in the coincidence scheme and very high degree of entanglement. The results are predicted theoretically and confirmed experimentally.

Spontaneous emission of a photon by an atom is described theoretically in three dimensions with the initial wave function of a finite-mass atom taken in the form of a finite-size wave packet. Recoil and wave-packet spreading are taken into account. The total atom-photon wave function is found in the momentum and coordinate representations as the solution of an initial-value problem. The atom-photon entanglement arising in such a process is shown to be closely related to the structure of atom and photon wave packets which can be measured in the coincidence and single-particle schemes of measurements. Two predicted effects, arising under the conditions of high entanglement, are anomalous narrowing of the coincidence wave packets and, under different conditions, anomalous broadening of the single-particle wave packets. Fundamental symmetry relations between the photon and atom single-particle and coincidence wave packet widths are established. The relationship with the famous scenario of Einstein-Podolsky-Rosen is discussed., 30 pages, 7 figures, Phys. Rev. A

We propose and experimentally demonstrate a method to prepare a nonspreading atomic wave packet. Our technique relies on a spatially modulated absorption constantly chiseling away from an initially broad de Broglie wave. The resulting contraction is balanced by dispersion due to Heisenberg's uncertainty principle. This quantum evolution results in the formation of a nonspreading wave packet of Gaussian form with a spatially quadratic phase. Experimentally, we confirm these predictions by observing the evolution of the momentum distribution. Moreover, by employing interferometric techniques, we measure the predicted quadratic phase across the wave packet. Nonspreading wave packets of this kind also exist in two space dimensions and we can control their amplitude and phase using optical elements., Comment: 4 figures

The narrowing of electron and ion wave packets in the process of photoionization is investigated, with the electron-ion recoil taken fully into account. Packet localization of this type is directly related to entanglement in the joint quantum state of the electron and ion, and to Einstein-Podolsky-Rosen localization. Experimental observation of such packet-narrowing effects is suggested via coincidence registration by two detectors, with a fixed position of one and varying position of the other. A similar effect, typically with an enhanced degree of entanglement, is shown to occur in the case of photodissociation of molecules.