Probing the circulation of ring-shaped Bose-Einstein condensates

This paper reports the results of a theoretical and experimental study of how the initial circulation of ring-shaped Bose-Einstein condensates (BECs) can be probed by time-of-flight (TOF) images. We have studied theoretically the dynamics of a BEC after release from a toroidal trap potential by solving the 3D Gross-Pitaevskii (GP) equation. The trap and condensate characteristics matched those of a recent experiment. The circulation, experimentally imparted to the condensate by stirring, was simulated theoretically by imprinting a linear azimuthal phase on the initial condensate wave function. The theoretical TOF images were in good agreement with the experimental data. We find that upon release the dynamics of the ring--shaped condensate proceeds in two distinct phases. First, the condensate expands rapidly inward, filling in the initial hole until it reaches a minimum radius that depends on the initial circulation. In the second phase, the density at the inner radius increases to a maximum after which the hole radius begins slowly to expand. During this second phase a series of concentric rings appears due to the interference of ingoing and outgoing matter waves from the inner radius. The results of the GP equation predict that the hole area is a quadratic function of the initial circulation when the condensate is released directly from the trap in which it was stirred and is a linear function of the circulation if the trap is relaxed before release. These scalings matched the data. Thus, hole size after TOF can be used as a reliable probe of initial condensate circulation. This connection between circulation and hole size after TOF will facilitate future studies of atomtronic systems that are implemented in ultracold quantum gases.Comment: 9 pages, 9 figure

Young\u27s Double-Slit Interferometry within an Atom

An experiment is described which is an analog of Young\u27s double-slit interferometer using an atomic electron instead of light. Two phase-coherent laser pulses are used to excite a single electron into a state of the form of a pair of Rydberg wave packets that are initially on opposite sides of the orbit. The two wave packets propagate and spread until they completely overlap, then a third phase-coherent laser pulse probes the resulting fringe pattern. The relative phase of the two wave packets is varied so that the interference produces a single localized electron wave packet on one side of the orbit or the other

Excitation of an Atomic Electron to a Coherent Superposition of Macroscopically Distinct States

An atomic electron is prepared in a state closely analogous to Schrödinger’s coherent superposition of “live cat” and “dead cat.” The electronic state is a coherent superposition of two spatially localized wave packets separated by approximately 0.4 mm at the opposite extremes of a Kepler orbit. State-selective ionization is used to verify that only every other atomic level is populated in the “cat state,” and a Ramsey fringe measurement is used to verify the coherence of the superposition

Young\u27s Double-Slit Interferometry within an Atom

An experiment is described which is an analog of Young\u27s double-slit interferometer using an atomic electron instead of light. Two phase-coherent laser pulses are used to excite a single electron into a state of the form of a pair of Rydberg wave packets that are initially on opposite sides of the orbit. The two wave packets propagate and spread until they completely overlap, then a third phase-coherent laser pulse probes the resulting fringe pattern. The relative phase of the two wave packets is varied so that the interference produces a single localized electron wave packet on one side of the orbit or the other

Phase and Risetime Dependence Using RF Pulses in Multiphoton Processes

With this experiment we demonstrate that excitation of a two-state system with radio-frequency fields differing in phase by 90° produces nonintuitively different results, even for very long pulses. In addition, we show how the phase dependence of the transition probability of long pulses can be easily understood by using the single cycle time propagator. Finally, we have found surprising results for real pulses in the strong-field regime, i.e., pulses having appreciable rise and fall times

Population Trapping in Extremely Highly Excited States in Microwave Ionization

When a lithium atom in a Rydberg state (n 80) is exposed to a short, intense microwave pulse we find that substantial population is left in extremely highly excited states (n . 120), in spite of the fact that the microwave field amplitude is more than 40 times larger than required to classically ionize these states

Phase and Risetime Dependence Using RF Pulses in Multiphoton Processes

With this experiment we demonstrate that excitation of a two-state system with radio-frequency fields differing in phase by 90° produces nonintuitively different results, even for very long pulses. In addition, we show how the phase dependence of the transition probability of long pulses can be easily understood by using the single cycle time propagator. Finally, we have found surprising results for real pulses in the strong-field regime, i.e., pulses having appreciable rise and fall times

Population Trapping in Extremely Highly Excited States in Microwave Ionization

When a lithium atom in a Rydberg state (n 80) is exposed to a short, intense microwave pulse we find that substantial population is left in extremely highly excited states (n . 120), in spite of the fact that the microwave field amplitude is more than 40 times larger than required to classically ionize these states

Frequency Modulated Excitation of a Two-Level Atom

We present a detailed experimental study of the frequency-modulated excitation of a two-level atom, using a microwave field to drive transitions between two Rydberg Stark states of potassium. In the absence of a modulation the interaction is the standard model of the Rabi problem, producing sinusoidal oscillations of the population between the two states. In the presence of a frequency modulation of the interacting field, however, the time evolution of the system is significantly modified, producing square wave oscillations of the popula- tion, sinusoidal oscillations at a different frequency, or even sinusoidal oscillations built up in a series of stair steps. The three responses described above are each found in a different regime for the frequency of the modulation with respect to the unmodulated Rabi frequency: the low-, high-, and intermediate-frequency regimes, respectively