T

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 that 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.

Atom-Chip Fountain Gravimeter.

We demonstrate a quantum gravimeter by combining the advantages of an atom chip for the generation, delta-kick collimation, and coherent manipulation of freely falling Bose-Einstein condensates (BECs) with an innovative launch mechanism based on Bloch oscillations and double Bragg diffraction. Our high-contrast BEC interferometer realizes tens of milliseconds of free fall in a volume as little as a one centimeter cube and paves the way for measurements with sub-µGal accuracies in miniaturized, robust devices.

Double Bragg Interferometry.

We employ light-induced double Bragg diffraction of delta-kick collimated Bose-Einstein condensates to create three symmetric Mach-Zehnder interferometers. They rely on (i) first-order, (ii) two successive first-order, and (iii) second-order processes which demonstrate the scalability of the corresponding momentum transfer. With respect to devices based on conventional Bragg scattering, these symmetric interferometers double the scale factor and feature a better suppression of noise and systematic uncertainties intrinsic to the diffraction process. Moreover, we utilize these interferometers as tiltmeters for monitoring their inclination with respect to gravity.

Composite-light-pulse technique for high-precision atom interferometry.

We realize beam splitters and mirrors for atom waves by employing a sequence of light pulses rather than individual ones. In this way we can tailor atom interferometers with improved sensitivity and accuracy. We demonstrate our method of composite pulses by creating a symmetric matter-wave interferometer which combines the advantages of conventional Bragg- and Raman-type concepts. This feature leads to an interferometer with a high immunity to technical noise allowing us to devise a large-area Sagnac gyroscope yielding a phase shift of 6.5 rad due to the Earth's rotation. With this device we achieve a rotation rate precision of 120 nrad s(-1) Hz(-1/2) and determine the Earth's rotation rate with a relative uncertainty of 1.2%.

Bound states in sharply bent waveguides: analytical and experimental approach.

Quantum wires and electromagnetic waveguides possess common features since their physics is described by the same wave equation. We exploit this analogy to investigate experimentally with microwave waveguides and theoretically with the help of an effective potential approach the occurrence of bound states in sharply bent quantum wires. In particular, we compute the bound states, study the features of the transition from a bound to an unbound state caused by the variation of the bending angle, and determine the critical bending angles at which such a transition takes place. The predictions are confirmed by calculations based on a conventional numerical method as well as experimental measurements of the spectra and electric field intensity distributions of electromagnetic waveguides.

Interferometry with Bose-Einstein condensates in microgravity.

Atom interferometers covering macroscopic domains of space-time are a spectacular manifestation of the wave nature of matter. Because of their unique coherence properties, Bose-Einstein condensates are ideal sources for an atom interferometer in extended free fall. In this Letter we report on the realization of an asymmetric Mach-Zehnder interferometer operated with a Bose-Einstein condensate in microgravity. The resulting interference pattern is similar to the one in the far field of a double slit and shows a linear scaling with the time the wave packets expand. We employ delta-kick cooling in order to enhance the signal and extend our atom interferometer. Our experiments demonstrate the high potential of interferometers operated with quantum gases for probing the fundamental concepts of quantum mechanics and general relativity.

A diffractive mechanism of focusing.

We examine the free time evolution of a rectangular one dimensional Schrödinger wave packet of constant phase during the early stage which in the paraxial wave approximation is identical to the diffraction of a scalar field from a single slit. Our analysis, based on numerics and the Cornu spiral reveals considerable intricate detail behavior in the density and phase of the wave. We also point out a concentration of the intensity that occurs on axis and propose a new measure of width that expresses this concentration.

Bose-Einstein condensation in microgravity.

Albert Einstein's insight that it is impossible to distinguish a local experiment in a "freely falling elevator" from one in free space led to the development of the theory of general relativity. The wave nature of matter manifests itself in a striking way in Bose-Einstein condensates, where millions of atoms lose their identity and can be described by a single macroscopic wave function. We combine these two topics and report the preparation and observation of a Bose-Einstein condensate during free fall in a 146-meter-tall evacuated drop tower. During the expansion over 1 second, the atoms form a giant coherent matter wave that is delocalized on a millimeter scale, which represents a promising source for matter-wave interferometry to test the universality of free fall with quantum matter.

Gauss sum factorization with cold atoms.

We report the first implementation of a Gauss sum factorization algorithm by an internal state Ramsey interferometer using cold atoms. A sequence of appropriately designed light pulses interacts with an ensemble of cold rubidium atoms. The final population in the involved atomic levels determines a Gauss sum. With this technique we factor the number N=263193.

Observation of nonspreading wave packets in an imaginary potential.

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.

Fresnel representation of the Wigner function: an operational approach.

We present an operational definition of the Wigner function. Our method relies on the Fresnel transform of measured Rabi oscillations and applies to motional states of trapped atoms as well as to field states in cavities. We illustrate this technique using data from recent experiments in ion traps [Phys. Rev. Lett. 76, 1796 (1996)]] and in cavity QED [Nature (London) 403, 743 (2000)]]. The values of the Wigner functions of the underlying states at the origin of phase space are W(|0>)(0)=+1.75 for the vibrational ground state and W(|1>)(0)=-1.4 for the one-photon number state. We generalize this method to wave packets in arbitrary potentials.

In- and outbound spreading of a free-particle s-wave.

We show that a free quantum particle in two dimensions with zero angular momentum (s wave) in the form of a ring-shaped wave packet feels an attraction towards the center of the ring, leading first to a contraction followed by an expansion. An experiment to demonstrate this effect is also outlined.

State reconstruction of the kicked rotor.

We propose two experimentally feasible methods based on atom interferometry to measure the quantum state of the kicked rotor.

Fractional Talbot effect in phase space: A compact summation formula.

A phase space description of the fractional Talbot effect, occurring in a one--dimensional Fresnel diffraction from a periodic grating, is presented. Using the phase space formalism a compact summation formula for the Wigner function at rational multiples of the Talbot distance is derived. The summation formula shows that the fractional Talbot image in the phase space is generated by a finite sum of spatially displaced Wigner functions of the source field.