arXiv subjects

N. T. Zinner

Publications and source records attributed to N. T. Zinner.

At least 109 records · Page 6Linked to original sources

arXiv2013

Dimensional Effects on the Momentum distribution of Bosonic Trimer States

The momentum distribution is a powerful probe of strongly-interacting systems that are expected to display universal behavior. This is contained in the contact parameters which relate few- and many-body properties. Here we consider a Bose gas in two dimensions and explicitly show that the two-body contact parameter is universal and then demonstrate that the momentum distribution at next-to-leading order has a logarithmic dependence on momentum which is vastly different from the three-dimensional case. Based on this, we propose a scheme for measuring the effective dimensionality of a quantum many-body system by exploiting the functional form of the momentum distribution.

cond-mat.quant-gas↗

arXiv2012

Virial expansion coefficients in the harmonic approximation

The virial expansion method is applied within a harmonic approximation to an interacting N-body system of identical fermions. We compute the canonical partition functions for two and three particles to get the two lowest orders in the expansion. The energy spectrum is carefully interpolated to reproduce ground state properties at low temperature and the non-interacting large temperature limit of constant virial coefficients. This resembles the smearing of shell effects in finite systems with increasing temperature. Numerical results are discussed for the second and third virial coefficients as function of dimension, temperature, interaction, and the transition temperature between low and high energy limits.

cond-mat.stat-mech↗

arXiv2012

Many-particle Systems in One Dimension in the Harmonic Approximation

We consider energetics and structural properties of a many particle system in one dimension with pairwise contact interactions confined in a parabolic external potential. To render the problem analytically solvable, we use the harmonic approximation scheme at the level of the Hamiltonian. We investigate the scaling with particle number of the ground state energies for systems consisting of identical bosons or fermions. We then proceed to focus on bosonic systems and make a detailed comparison to known exact results in the absence of the parabolic external trap for three-body systems. We also consider the thermodynamics of the harmonic model which turns out to be similar for bosons and fermions due to the lack of degeneracy in one dimension.

cond-mat.quant-gas↗

arXiv2012

Efimov Physics and the Three-Body Parameter within a Two-Channel Framework

We calculate shallow three-body bound states in the universal regime, defined by Efimov, with inclusion of both scattering length and effective range parameters. The universal spectrum is recovered for the least bound states, whereas for larger binding energies we find corrections to the universal scaling laws. We recover known results for broad Feshbach resonances with small effective range, whereas in the case of narrow resonances we find a distinct non-monotonic behavior of the threshold at which the lowest Efimov trimer merges with the three-body continuum. To address the issue of the physical origin of the three-body parameter we provide a physically clear model for the relation between three-body physics and typical two-body atom-atom interactions. Our results demonstrate that experimental information from narrow Feshbach resonances and/or mixed systems are of vital importance to pin down the relation of two- and three-body physics in atomic systems.

cond-mat.quant-gas↗

arXiv2012

Density wave instabilities of tilted fermionic dipoles in a multilayer geometry

We consider the density wave instability of fermionic dipoles aligned by an external field, and moving in equidistant layers at zero temperature. Using a conserving Hartree-Fock approximation, we show that correlations between dipoles in different layers significantly decrease the critical coupling strength for the formation of density waves when the distance between the layers is comparable to the inter-particle distance within each layer. This effect, which is strongest when the dipoles are oriented perpendicular to the planes, causes the density waves in neighboring layers to be in-phase for all orientations of the dipoles. We furthermore demonstrate that the effects of the interlayer interaction can be understood from a classical model. Finally, we show that the interlayer correlations are important for experimentally relevant dipolar molecules, including the chemically stable $^{23}$Na$^{40}$K and $^{40}$K$^{133}$Cs, where the density wave regime is within experimental reach.

cond-mat.quant-gas↗

arXiv2012

Effective Potential for Ultracold Atoms at the Zero-Crossing of a Feshbach Resonance

We consider finite-range effects when the scattering length goes to zero near a magnetically controlled Feshbach resonance. The traditional effective-range expansion is badly behaved at this point and we therefore introduce an effective potential that reproduces the full T-matrix. To lowest order the effective potential goes as momentum squared times a factor that is well-defined as the scattering length goes to zero. The potential turns out to be proportional to the background scattering length squared times the background effective range for the resonance. We proceed to estimate the applicability and relative importance of this potential for Bose-Einstein condensates and for two-component Fermi gases where the attractive nature of the effective potential can lead to collapse above a critical particle number or induce instability toward pairing and superfluidity. For broad Feshbach resonances the higher-order effect is completely negligible. However, for narrow resonances in tightly confined samples signatures might be experimentally accessible. This could be relevant for sub-optical wavelength microstructured traps at the interface of cold atoms and solid-state surfaces.

cond-mat.quant-gas↗

arXiv2012

Field-induced long-lived supermolecules

We demonstrate that the long-lived bound states (super-molecules) can exist in the dilute limit when we tune the shape of effective potential between polar molecules by an external microwave field. Binding energies, average sizes, and phase diagrams for both s-orbital (bosons) and p-orbital (fermions) dimers are studied, together with bosonic trimer states. We explicitly show that the non- adiabatic transition rate can be easily tuned small for such ground state super-molecules, so that the system can be stable from collapse even near the associated potential resonance. Our results, therefore, suggest a feasible cold molecule system to investigate both novel few-body and many-body physics (for example, the p-wave BCS-BEC crossover for fermions and the paired condensate for bosons) that can not be easily accessed in single species atomic gases.

cond-mat.quant-gas↗

arXiv2012

Analytic Harmonic Approach to the N-body problem

We consider an analytic way to make the interacting N-body problem tractable by using harmonic oscillators in place of the relevant two-body interactions. The two body terms of the N-body Hamiltonian are approximated by considering the energy spectrum and radius of the relevant two-body problem which gives frequency, center position, and zero point energy of the corresponding harmonic oscillator. Adding external harmonic one-body terms, we proceed to solve the full quantum mechanical N-body problem analytically for arbitrary masses. Energy eigenvalues, eigenmodes, and correlation functions like density matrices can then be computed analytically. As a first application of our formalism, we consider the N-boson problem in two- and three dimensions where we fit the two-body interactions to agree with the well-known zero-range model for two particles in a harmonic trap. Subsequently, condensate fractions, spectra, radii, and eigenmodes are discussed as function of dimension, boson number N, and scattering length obtained in the zero-range model. We find that energies, radii, and condensate fraction increase with scattering length as well as boson number, while radii decrease with increasing boson number. Our formalism is completely general and can also be applied to fermions, Bose-Fermi mixtures, and to more exotic geometries.

cond-mat.quant-gas↗

arXiv2012

Universal Two-Body Spectra of Ultracold Harmonically Trapped Atoms in Two and Three Dimensions

We consider the spectrum of two ultracold harmonically trapped atoms interacting via short-range interactions. The Green's function approach is used to unify the two and three dimensional cases. We derive criteria for the universality of the spectrum, i.e. its independence of the details of the short-range interaction. The results in three dimensions are examplified for narrow s-wave Feshbach resonances and we show how effective range corrections can modify the rearrangement of the level structure. However, this requires extremely narrow resonances or very tight traps that are not currently experimentally available. In the two-dimensional case we discuss the p-wave channel in detail and demonstrate how the non-universality of the spectrum arises within the Green's function approach. We then show that the spectrum is not particularly sensitive to the short-distance details in the case when the two-body interaction has a bound state.

cond-mat.quant-gas↗

arXiv2012

Bound Chains of Tilted Dipoles in Layered Systems

Ultracold polar molecules in multilayered systems have been experimentally realized very recently. While experiments study these systems almost exclusively through their chemical reactivity, the outlook for creating and manipulating exotic few- and many-body physics in dipolar systems is fascinating. Here we concentrate on few-body states in a multilayered setup. We exploit the geometry of the interlayer potential to calculate the two- and three-body chains with one molecule in each layer. The focus is on dipoles that are aligned at some angle with respect to the layer planes by means of an external eletric field. The binding energy and the spatial structure of the bound states are studied in several different ways using analytical approaches. The results are compared to stochastic variational calculations and very good agreement is found. We conclude that approximations based on harmonic oscillator potentials are accurate even for tilted dipoles when the geometry of the potential landscape is taken into account.

quant-ph↗

arXiv2012

Layers of Cold Dipolar Molecules in the Harmonic Approximation

We consider the N-body problem in a layered geometry containing cold polar molecules with dipole moments that are polarized perpendicular to the layers. A harmonic approximation is used to simplify the hamiltonian and bound state properties of the two-body inter-layer dipolar potential are used to adjust this effective interaction. To model the intra-layer repulsion of the polar molecules, we introduce a repulsive inter-molecule potential that can be parametrically varied. Single chains containing one molecule in each layer, as well as multi-chain structures in many layers are discussed and their energies and radii determined. We extract the normal modes of the various systems as measures of their volatility and eventually of instability, and compare our findings to the excitations in crystals. We find modes that can be classified as either chains vibrating in phase or as layers vibrating against each other. The former correspond to acoustic and the latter to optical phonons. Instabilities can occur for large intra-layer repulsion and produce diverging amplitudes of molecules in the outer layers. Lastly, we consider experimentally relevant regimes to observe the structures.

cond-mat.quant-gas↗

arXiv2012

Few-body bound state stability of dipolar molecules in two dimensions

Bound structures among dipolar molecules in multilayers are a topic of great interest in the light of recent experiments that have demonstrated the feasibility of the setup. While it is known that two molecules in two adjacent layers will always bind, larger complexes have only been scarcely addressed thus far. Here we prove rigorously that three- and four-body states will never be bound when the dipoles are oriented perpendicular to the layers. The technique employed is general and can be used for more molecules/layers and other geometries. Our analytical findings are supported by numerical calculations for both fermionic and bosonic molecules. Furthermore, we calculate the reduction in intralayer repulsion necessary to bind large complexes and estimate the influence of bound complexes in systems with many layers.

cond-mat.quant-gas↗

arXiv2012

A supercircle description of universal three-body states in two dimensions

We consider bound states of asymmetric three-body systems confined to two dimensions. In the universal regime, two energy ratios and two mass ratios provide complete knowledge of the three-body energy measured in units of one two-body energy. The lowest number of stable bound states is produced when one mass is larger than two similar masses. We focus on selected asymmetric systems of interest in cold atom physics. The scaled three-body energy and the two scaled two-body energies are related through an equation for a supercircle whose radius increases almost linearly with three-body energy. The exponents exhibit an increasing behavior with three-body energy. The mass dependence is highly non-trivial. We give a simple relation that predicts the universal three-body energy.

cond-mat.quant-gas↗

arXiv2012

BCS-BEC Crossover in Bilayers of Cold Fermionic Polar Molecules

We investigate the quantum and thermal phase diagram of fermionic polar molecules loaded in a bilayer trapping potential with perpendicular dipole moment. We use both a BCS theory approach that is most realiable at weak-coupling and a strong-coupling approach that considers the two-body bound dimer states with one molecules in each layer as the relevant degree of freedom. The system ground state is a Bose-Einstein condensate (BEC) of dimer bound states in the low density limit and a paired superfluid (BCS) state in the high density limit. At zero temperature, the intralayer repulsion is found to broaden the regime of BCS-BEC crossover, and can potentially induce system collapse through the softening of roton excitations. The BCS theory and the strongly-coupled dimer picture yield similar predictions for the parameters of the crossover regime. The BKT transition temperature of the dimer superfluid is also calculated. The crossover can be driven by many-body effects and is strongly affected by the intralayer interaction which was ignored in previous studies.

cond-mat.quant-gas↗

arXiv2012

Dimers, Effective Interactions, and Pauli Blocking Effects in a Bilayer of Cold Fermionic Polar Molecules

We consider a bilayer setup with two parallel planes of cold fermionic polar molecules when the dipole moments are oriented perpendicular to the planes. The binding energy of two-body states with one polar molecule in each layer is determined and compared to various analytic approximation schemes in both coordinate- and momentum-space. The effective interaction of two bound dimers is obtained by integrating out the internal dimer bound state wave function and its robustness under analytical approximations is studied. Furthermore, we consider the effect of the background of other fermions on the dimer state through Pauli blocking, and discuss implications for the zero-temperature many-body phase diagram of this experimentally realizable system.

cond-mat.quant-gas↗

arXiv2011

Quantum Statistics and Thermodynamics in the Harmonic Approximation

We describe a method to compute thermodynamic quantities in the harmonic approximation for identical bosons and fermions in an external confining field. We use the canonical partition function where only energies and their degeneracies enter. The number of states of given energy and symmetry is found by separating the center of mass motion, and counting the remaining states of given symmetry and excitation energy of the relative motion. The oscillator frequencies that enter the harmonic Hamiltonian can be derived from realistic model parameters and the method corresponds to an effective interaction approach based on harmonic interactions. To demonstrate the method, we apply it to systems in two dimensions. Numerical calculations are compared to a brute force method that is considerably more computationally intensive.

quant-ph↗

arXiv2011

Few-Body Bound Complexes in One-dimensional Dipolar Gases and Non-Destructive Optical Detection

We consider dipolar interactions between heteronuclear molecules in low-dimensional geometries. The setup consists of two one-dimensional tubes. We study the stability of possible few-body complexes in the regime of repulsive intratube interaction, where the binding arises from intertube attraction. The stable dimers, trimers, and tetramers are found and we discuss their properties for both bosonic and fermionic molecules. To observe these complexes we propose an optical non-destructive detection scheme that enables in-situ observation of the creation and dissociation of the few-body complexes. A detailed description of the expected signal of such measurements is given using the numerically calculated wave functions of the bound states. We also discuss implications on the many-body physics of dipolar systems in tubular geometries, as well as experimental issues related to the external harmonic confinement along the tube and the prospect of applying an in-tube optical lattice to increase the effective dipole strength.

cond-mat.quant-gas↗

arXiv2011

Scaling and universality in two dimensions: three-body bound states with short-ranged interactions

The momentum space zero-range model is used to investigate universal properties of three interacting particles confined to two dimensions. The pertinent equations are first formulated for a system of two identical and one distinct particle and the two different two-body subsystems are characterized by two-body energies and masses. The three-body energy in units of one of the two-body energies is a universal function of the other two-body energy and the mass ratio. We derive convenient analytical formulae for calculations of the three-body energy as function of these two independent parameters and exhibit the results as universal curves. In particular, we show that the three-body system can have any number of stable bound states. When the mass ratio of the distinct to identical particles is greater than 0.22 we find that at most two stable bound states exist, while for two heavy and one light mass an increasing number of bound states is possible. The specific number of stable bound states depends on the ratio of two-body bound state energies and on the mass ratio and we map out an energy-mass phase-diagram of the number of stable bound states. Realizable systems of both fermions and bosons are discussed in this framework.

cond-mat.quant-gas↗