Coherent Particle Transfer in an On-Demand Single-Electron Source

Coherent electron transfer from a localized state trapped in a quantum dot into a ballistic conductor, taking place in on-demand electron sources, in general may result in excitation of particle-hole pairs. We consider a simple model for these effects, involving a resonance level with time-dependent energy, and derive Floquet scattering matrix describing inelastic transitions of particles in the Fermi sea. We find that, as the resonance level is driven through the Fermi level, particle transfer may take place completely without particle-hole excitations for certain driving protocols. In particular, such noiseless transfer occurs when the level moves with constant rapidity, its energy changing linearly with time. A detection scheme for studying the coherence of particle transfer is proposed.Comment: 5 pages, 3 figures. Updated introduction, Fig. 1, and reference

Counterintuitive transitions in the multistate Landau-Zener problem with linear level crossings

We generalize the Brundobler-Elser hypothesis in the multistate Landau-Zener problem to the case when instead of a state with the highest slope of the diabatic energy level there is a band of states with an arbitrary number of parallel levels having the same slope. We argue that the probabilities of counterintuitive transitions among such states are exactly zero.Comment: 9 pages, 5 figure

Non-divergent pseudo-potential treatment of spin-polarized fermions under 1D and 3D harmonic confinement

Atom-atom scattering of bosonic one-dimensional (1D) atoms has been modeled successfully using a zero-range delta-function potential, while that of bosonic 3D atoms has been modeled successfully using Fermi-Huang's regularized s-wave pseudo-potential. Here, we derive the eigenenergies of two spin-polarized 1D fermions under external harmonic confinement interacting through a zero-range potential, which only acts on odd-parity wave functions, analytically. We also present a divergent-free zero-range potential treatment of two spin-polarized 3D fermions under harmonic confinement. Our pseudo-potential treatments are verified through numerical calculations for short-range model potentials.Comment: 9 pages, 4 figures (subm. to PRA on 03/15/2004

Quantum theory of an atom laser originating from a Bose-Einstein condensate or a Fermi gas in the presence of gravity

We present a 3D quantum mechanical theory of radio-frequency outcoupled atom lasers from trapped atomic gases in the presence of the gravitational force. Predictions for the total outcoupling rate as a function of the radio-frequency and for the beam wave function are given. We establish a sum rule for the energy integrated outcoupling, which leads to a separate determination of the coupling strength between the atoms and the radiation field. For a non-interacting Bose-Einstein condensate analytic solutions are derived which are subsequently extended to include the effects of atomic interactions. The interactions enhance interference effects in the beam profile and modify the outcoupling rate of the atom laser. We provide a complete quantum mechanical solution which is in line with experimental findings and allows to determine the validity of commonly used approximative methods. We also extend the formalism to a fermionic atom laser and analyze the effect of superfluidity on the outcoupling of atoms.Comment: 13 pages, 8 figures, slightly expanded versio

Stable Heteronuclear Few-Atom Bound States in Mixed Dimensions

We study few-body problems in mixed dimensions with $N \ge 2$ heavy atoms trapped individually in parallel one-dimensional tubes or two-dimensional disks, and a single light atom travels freely in three dimensions. By using the Born-Oppenheimer approximation, we find three- and four-body bound states for a broad region of heavy-light atom scattering length combinations. Specifically, the existence of trimer and tetramer states persist to negative scattering lengths regime, where no two-body bound state is present. These few-body bound states are analogous to the Efimov states in three dimensions, but are stable against three-body recombination due to geometric separation. In addition, we find that the binding energy of the ground trimer and tetramer state reaches its maximum value when the scattering lengths are comparable to the separation between the low-dimensional traps. This resonant behavior is a unique feature for the few-body bound states in mixed dimensions.Comment: Extended version with 14 pages and 14 figure

Mean-field dynamics of a Bose-Einstein condensate in a time-dependent triple-well trap: Nonlinear eigenstates, Landau-Zener models and STIRAP

We investigate the dynamics of a Bose--Einstein condensate (BEC) in a triple-well trap in a three-level approximation. The inter-atomic interactions are taken into account in a mean-field approximation (Gross-Pitaevskii equation), leading to a nonlinear three-level model. New eigenstates emerge due to the nonlinearity, depending on the system parameters. Adiabaticity breaks down if such a nonlinear eigenstate disappears when the parameters are varied. The dynamical implications of this loss of adiabaticity are analyzed for two important special cases: A three level Landau-Zener model and the STIRAP scheme. We discuss the emergence of looped levels for an equal-slope Landau-Zener model. The Zener tunneling probability does not tend to zero in the adiabatic limit and shows pronounced oscillations as a function of the velocity of the parameter variation. Furthermore we generalize the STIRAP scheme for adiabatic coherent population transfer between atomic states to the nonlinear case. It is shown that STIRAP breaks down if the nonlinearity exceeds the detuning.Comment: RevTex4, 7 pages, 11 figures, content extended and title/abstract change

Degenerate Landau-Zener model: Exact analytical solution

The exact analytical solution of the degenerate Landau-Zener model, wherein two bands of degenerate energies cross in time, is presented. The solution is derived by using the Morris-Shore transformation, which reduces the fully coupled system to a set of independent nondegenerate two-state systems and a set of decoupled states. Due to the divergence of the phase of the off-diagonal element of the propagator in the original Landau-Zener model, not all transition probabilities exist for infinite time duration. In general, apart from some special cases, only the transition probabilities between states within the same degenerate set exist, but not between states of different sets. An illustration is presented for the transition between the magnetic sublevels of two atomic levels with total angular momenta J=2 and 1

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.Comment: 10 pages, 5 eps figure

Counterintuitive transitions between crossing energy levels

We calculate analytically the probabilities for intuitive and counterintuitive transitions in a three-state system, in which two parallel energies are crossed by a third, tilted energy. The state with the tilted energy is coupled to the other two states in a chainwise linkage pattern with constant couplings of finite duration. The probability for a counterintuitive transition is found to increase with the square of the coupling and decrease with the squares of the interaction duration, the energy splitting between the parallel energies, and the tilt (chirp) rate. Physical examples of this model can be found in coherent atomic excitation and optical shielding in cold atomic collisions

Dissipative Landau-Zener transitions of a qubit: bath-specific and universal behavior

We study Landau-Zener transitions in a qubit coupled to a bath at zero temperature. A general formula is derived that is applicable to models with a non-degenerate ground state. We calculate exact transition probabilities for a qubit coupled to either a bosonic or a spin bath. The nature of the baths and the qubit-bath coupling is reflected in the transition probabilities. For diagonal coupling, when the bath causes energy fluctuations of the diabatic qubit states but no transitions between them, the transition probability coincides with the standard LZ probability of an isolated qubit. This result is universal as it does not depend on the specific type of bath. For pure off-diagonal coupling, by contrast, the tunneling probability is sensitive to the coupling strength. We discuss the relevance of our results for experiments on molecular nanomagnets, in circuit QED, and for the fast-pulse readout of superconducting phase qubits.Comment: 16 pages, 8 figure