arXiv subjects

Thorsten Koehler

Publications and source records attributed to Thorsten Koehler.

At least 19 recordsLinked to original sources

arXiv2007

Excited Thomas-Efimov levels in ultracold gases

Since the early days of quantum physics, the complex behavior of three interacting particles has been the subject of numerous experimental and theoretical studies. In a recent Letter to Nature, Kraemer et al. [Nature (London) 440, 315 (2006)] report on experimental ``evidence for Efimov quantum states'' in an ultracold gas of cesium atoms. Such quantum states refer to an infinite series of energy levels of three identical Bose particles, accumulating at the threshold for dissociation as the scattering length of each pair is tuned to infinity. Whereas the existence of a single Efimov state has been predicted for three helium atoms, earlier experimental studies concluded that this elusive state had not been found. In this paper we show by an intuitive argument and full numerical calculations that the helium and cesium experiments actually provide evidence of the same, ground state of this trimer spectrum, which the helium experimentalists and pioneering theoretical studies had not associated with Efimov's effect. Unlike the helium trimer, the observed 133Cs_3 resonance refers to a Borromean molecular state. We discuss how as yet unobserved, excited Efimov quantum states might be detected in ultracold gases of 85Rb and of 133Cs at magnetic field strengths in the vicinity of 0.08 T (800 G).

cond-mat.other↗

arXiv2006

Association of molecules using a resonantly modulated magnetic field

We study the process of associating molecules from atomic gases using a magnetic field modulation that is resonant with the molecular binding energy. We show that maximal conversion is obtained by optimising the amplitude and frequency of the modulation for the particular temperature and density of the gas. For small modulation amplitudes, resonant coupling of an unbound atom pair to a molecule occurs at a modulation frequency corresponding to the sum of the molecular binding energy and the relative kinetic energy of the atom pair. An atom pair with an off-resonant energy has a probability of association which oscillates with a frequency and time-varying amplitude which are primarily dependent on its detuning. Increasing the amplitude of the modulation tends to result in less energetic atom pairs being resonantly coupled to the molecular state, and also alters the dynamics of the transfer from continuum states with off-resonant energies. This leads to maxima and minima in the total conversion from the gas as a function of the modulation amplitude. Increasing the temperature of the gas leads to an increase in the modulation frequency providing the best fit to the thermal distribution, and weakens the resonant frequency dependence of the conversion. Mean-field effects can alter the optimal modulation frequency and lead to the excitation of higher modes. Our simulations predict that resonant association can be effective for binding energies of order $h \times 1$ MHz.

cond-mat.other↗

arXiv2006

Production of cold molecules via magnetically tunable Feshbach resonances

Magnetically tunable Feshbach resonances were employed to associate cold diatomic molecules in a series of experiments involving both atomic Bose as well as two spin component Fermi gases. This review illustrates theoretical concepts of both the particular nature of the highly excited Feshbach molecules produced and the techniques for their association from unbound atom pairs. Coupled channels theory provides the rigorous formulation of the microscopic physics of Feshbach resonances in cold gases. Concepts of dressed versus bare energy states, universal properties of Feshbach molecules, as well as the classification in terms of entrance- and closed-channel dominated resonances are introduced on the basis of practical two-channel approaches. Their significance is illustrated for several experimental observations, such as binding energies and lifetimes with respect to collisional relaxation. Molecular association and dissociation are discussed in the context of techniques involving linear magnetic field sweeps in cold Bose and Fermi gases as well as pulse sequences leading to Ramsey-type interference fringes. Their descriptions in terms of Landau-Zener, two-level mean field as well as beyond mean field approaches are reviewed in detail, including the associated ranges of validity.

cond-mat.other↗

arXiv2006

Classification of zero-energy resonances by dissociation of Feshbach molecules

We study the dissociation of Feshbach molecules by a magnetic field sweep across a zero-energy resonance. In the limit of an instantaneous magnetic field change, the distribution of atomic kinetic energy can have a peak indicating dominance of the molecular closed-channel spin configuration over the entrance channel. The extent of this dominance influences physical properties such as stability with respect to collisions, and so the readily measurable presence or absence of the corresponding peak provides a practical method of classifying zero-energy resonances. Currently achievable ramp speeds, e.g. those demonstrated by Duerr et al. [Phys. Rev. A 70, 031601 (2005)], are fast enough to provide magnetic field changes that may be interpreted as instantaneous. We study the transition from sudden magnetic field changes to asymptotically wide, linear ramps. In the latter limit, the predicted form of the atomic kinetic energy distribution is independent of the specific implementation of the two-body physics, provided that the near-resonant scattering properties are properly accounted for.

cond-mat.other↗

arXiv2005

Production of three-body Efimov molecules in an optical lattice

We study the possibility of associating meta-stable Efimov trimers from three free Bose atoms in a tight trap realised, for instance, via an optical lattice site or a microchip. The suggested scheme for the production of these molecules is based on magnetically tunable Feshbach resonances and takes advantage of the Efimov effect in three-body energy spectra. Our predictions on the energy levels and wave functions of three pairwise interacting 85Rb atoms rely upon exact solutions of the Faddeev equations and include the tightly confining potential of an isotropic harmonic atom trap. The magnetic field dependence of these energy levels indicates that it is the lowest energetic Efimov trimer state that can be associated in an adiabatic sweep of the field strength. We show that the binding energies and spatial extents of the trimer molecules produced are comparable, in their magnitudes, to those of the associated diatomic Feshbach molecule. The three-body molecular state follows Efimov's scenario when the pairwise attraction of the atoms is strengthened by tuning the magnetic field strength.

cond-mat.other↗

arXiv2005

Conventional character of the BCS-BEC cross-over in ultra-cold gases of 40K

We use the standard fermionic and boson-fermion Hamiltonians to study the BCS-BEC cross-over near the 202 G resonance in a two-component mixture of fermionic 40K atoms employed in the experiment of C.A. Regal et al., Phys. Rev. Lett. 92, 040403 (2004). Our mean-field analysis of many-body equilibrium quantities shows virtually no differences between the predictions of the two approaches, provided they are both implemented in a manner that properly includes the effect of the highest excited bound state of the background scattering potential, rather than just the magnetic-field dependence of the scattering length. Consequently, we rule out the macroscopic occupation of the molecular field as a mechanism behind the fermionic pair condensation and show that the BCS-BEC cross-over in ultra-cold 40K gases can be analysed and understood on the same basis as in the conventional systems of solid state physics.

cond-mat.supr-con↗

arXiv2005

Ramsey interferometry with atoms and molecules: two-body versus many-body phenomena

We discuss the frequency and visibility of atom-molecule Ramsey fringes observed in recent experiments by Claussen et al.[Phys. Rev. A 67, 060701 (2003)]. In these experiments a 85Rb Bose-Einstein condensate was exposed to a sequence of magnetic field pulses on the high field side of the 155 G Feshbach resonance. The observed oscillation frequencies largely agree with the theoretically predicted magnetic field dependence of the binding energy of the highest excited diatomic vibrational state, except for a small region very close to the singularity of the scattering length. Our analytic treatment of the experiment, as well as our dynamical simulations, follow the magnitude of the measured oscillation frequencies as well as the visibilities of the Ramsey fringes. We show that significant deviations from a purely binary dynamics, with an associated binding frequency, occur when the spatial extent of the molecular wave function becomes comparable with the mean distance between the atoms in the dilute gas. The experiments thus clearly identify the conditions under which diatomic molecules may be identified as a separate entity of the gas or, conversely, when the concept of binary physics in a many-body environment is bound to break down.

cond-mat.other↗

arXiv2005

Spontaneous dissociation of long-range Feshbach molecules

We study the spontaneous dissociation of diatomic molecules produced in cold atomic gases via magnetically tunable Feshbach resonances. We provide a universal formula for the lifetime of these molecules that relates their decay to the scattering length and the loss rate constant for inelastic spin relaxation. Our universal treatment as well as our exact coupled channels calculations for $^{85}$Rb dimers predict a suppression of the decay over several orders of magnitude when the scattering length is increased. Our predictions are in good agreement with recent measurements of the lifetime of $^{85}$Rb$_2$.

cond-mat.other↗

arXiv2004

Molecular production in two-component atomic Fermi gases

We provide a practical approach to the molecular production via linear downward sweeps of Feshbach resonances in degenerate Fermi gases containing incoherent mixtures of two atomic spin states. We show that the efficiency of the association of atoms is determined just by the Landau-Zener parameter in addition to the density of the gas. Our approach of pairwise summation of the microscopic binary transition probabilities leads to an intuitive explanation for the observed saturation of the molecular production and recovers all atomic loss curves of C.A. Regal et al. [Nature (London) 427, 47 (2003)] as well as K.E. Strecker et al. [Phys. Rev. Lett. 91, 080406 (2003)] without adjustable parameters.

cond-mat.other↗

arXiv2004

Heating and atom loss during upward ramps of Feshbach resonance levels in Bose-Einstein condensates

The production of pairs of fast atoms leads to a pronounced loss of atoms during upward ramps of Feshbach resonance levels in dilute Bose-Einstein condensates. We provide comparative studies on the formation of these bursts of atoms containing the physical predictions of several theoretical approaches at different levels of approximation. We show that despite their very different description of the microscopic binary physics during the passage of a Feshbach resonance, all approaches lead to virtually the same prediction on the total loss of condensate atoms, provided that the ramp of the magnetic field strength is purely linear. We give the reasons for this remarkable insensitivity of the remnant condensate fraction to the microscopic physical processes and compare the theoretical predictions with recent Feshbach resonance crossing experiments on 23Na and 85Rb.

cond-mat.other↗

arXiv2004

Adiabatic association of ultracold molecules via magnetic field tunable interactions

We consider in detail the situation of applying a time dependent external magnetic field to a 87Rb atomic Bose-Einstein condensate held in a harmonic trap, in order to adiabatically sweep the interatomic interactions across a Feshbach resonance to produce diatomic molecules. To this end, we introduce a minimal two-body Hamiltonian depending on just five measurable parameters of a Feshbach resonance, which accurately determines all low energy binary scattering observables, in particular, the molecular conversion efficiency of just two atoms. Based on this description of the microscopic collision phenomena, we use the many-body theory of T. Koehler and K. Burnett [Phys. Rev. A 65, 033601 (2002)] to study the efficiency of the association of molecules in a 87Rb Bose-Einstein condensate during a linear passage of the magnetic field strength across the 100 mT Feshbach resonance. We explore different, experimentally accessible, parameter regimes, and compare the predictions of Landau-Zener, configuration interaction, and two level mean field calculations with those of the microscopic many-body approach. Our comparative studies reveal a remarkable insensitivity of the molecular conversion efficiency with respect to both the details of the microscopic binary collision physics and the coherent nature of the Bose-Einstein condensed gas, provided that the magnetic field strength is varied linearly. We provide the reasons for this universality of the molecular production achieved by linear ramps of the magnetic field strength, and identify the Landau-Zener coefficient determined by F.H. Mies et al. [Phys. Rev. A 61, 022721 (2000)] as the main parameter that controls the efficiency.

cond-mat↗

arXiv2004

Dynamics of correlations in atomic Bose-Einstein condensates

The Gross-Pitaevskii equation has been extremely successful in the theory of weakly-interacting Bose-Einstein condensates. However, present-day experiments reach beyond the regime of its validity due to the significant role of correlations. We review a method of tackling the dynamics of correlations in Bose condensed gases, in terms of noncommutative cumulants. This new approach has a wide range of applicability in the areas of current interest, e.g. the production of molecules and the manipulation of interactions in condensates. It also offers an interesting perspective on the classical-field methods for partly condensed Bose gases.

cond-mat↗

arXiv2003

The nature of Feshbach molecules in Bose-Einstein condensates

We discuss the long range nature of the molecules produced in recent experiments on molecular Bose-Einstein condensation. The properties of these molecules depend on the full two-body Hamiltonian and not just on the states of the system in the absence of interchannel couplings. The very long range nature of the state is crucial to the efficiency of production in the experiments. Our many-body treatment of the gas accounts for the full binary physics and describes properly how these molecular condensates can be directly probed.

cond-mat↗

arXiv2003

Diffraction of Weakly Bound Clusters: Spectroscopy and Size Effects

Exciting experiments in the field of atom and molecule optics have lately drawn much attention to the effects involved in the coherent diffraction of particle beams. We review the influence of the finite size of the particles and of their energy level spectrum on the diffraction pattern. In turn, we demonstrate how experimental diffraction measurements allow to determine these quantities of weakly bound molecules by considering the diffraction of the dimer and trimer of helium, and the deuterium molecule dimer.

quant-ph↗

arXiv2002

Inelastic Diffraction and Spectroscopy of Very Weakly Bound Clusters

We study the coherent inelastic diffraction of very weakly bound two body clusters from a material transmission grating. We show that internal transitions of the clusters can lead to new separate peaks in the diffraction pattern whose angular positions determine the excitation energies. Using a quantum mechanical approach to few body scattering theory we determine the relative peak intensities for the diffraction of the van der Waals dimers (D_2)_2 and H_2-D_2. Based on the results for these realistic examples we discuss the possible applications and experimental challenges of this coherent inelastic diffraction technique.

quant-ph↗

arXiv2002

Three body problem in a dilute Bose-Einstein condensate

We derive the explicit three body contact potential for a dilute condensed Bose gas from microscopic theory. The three body coupling constant exhibits the general form predicted by T.T. Wu [Phys. Rev. 113, 1390 (1959)] and is determined in terms of the amplitudes of two and three body collisions in vacuum. In the present form the coupling constant becomes accessible to quantitative studies which should provide the crucial link between few body collisions and the stability of condensates with attractive two body forces.

cond-mat↗

arXiv2002

Microscopic theory of atom-molecule oscillations in a Bose-Einstein condensate

In a recent experiment at JILA [E.A. Donley et al., Nature (London) 417, 529 (2002)] an initially pure condensate of Rb-85 atoms was exposed to a specially designed time dependent magnetic field pulse in the vicinity of a Feshbach resonance. The production of new components of the gas as well as their oscillatory behavior have been reported. We apply a microscopic theory of the gas to identify these components and determine their physical properties. Our time dependent studies allow us to explain the observed dynamic evolution of all fractions, and to identify the physical relevance of the pulse shape. Based on ab initio predictions, our theory strongly supports the view that the experiments have produced a molecular condensate.

cond-mat↗

arXiv2002

The van der Waals Potential between Metastable Atoms and Solid Surfaces: Novel Diffraction Experiments versus Theory

Highly polarizable metastable He* ($\mathrm{2^3S}$) and Ne* ($\mathrm{2^3P}$) atoms have been diffracted from a 100 nm period silicon nitride transmission grating and the van der Waals coefficients $C_3$ for the interaction of the excited atoms with the silicon nitride surface have been determined from the diffraction intensities out to the 10th order. The results agree with calculations based on the non-retarded Lifshitz formula.

quant-ph↗