Standing-wave Pulses Research Articles

Ultrafast Kapitza-Dirac effect.

Similar to the optical diffraction of light passing through a material grating, the Kapitza-Dirac effect occurs when an electron is diffracted by a standing light wave. In its original description, the effect is time independent. Here, we extended the Kapitza-Dirac effect to the time domain. By tracking the spatiotemporal evolution of a pulsed electron wave packet diffracted by a 60-femtosecond (where one femtosecond = 10-15 seconds) standing wave pulse in a pump-probe scheme, we observed time-dependent diffraction patterns. The fringe spacing in the observed pattern differs from that generated by the conventional Kapitza-Dirac effect. By exploiting this time-resolved diffraction scheme, we can access the time evolution of the phase properties of a free electron and potentially image ionic potentials and electronic decoherences.

Fast and selective interband transfer of ultracold atoms in bichromatic lattices permitting Dirac points

An experimental group at Beijing[Yueyang Zhai, ${\it et. al.}$, Phys. Rev. A ${\bf 87}$, 063638 (2013)] introduced the method of standing-wave pulse sequence for efficiently preparing ultracold bosonic atoms into a specific excited band in a 1-dimensional optical lattice. Here, we report a theoretical extension of their work to the problem of 1-dimensional bichromatic superlattice. We find that varying the lattice parameters leads to the so-called Dirac point where a pair of excited bands crosses. This paper thus discusses ${\it simultaneously}$ the efficient excitation of the wave packet to the proximity of the Dirac point and its subsequent dynamics in the force field of a parabolic trap. With the aid of a toy model, we theoretically unravel the mechanism of the efficient preparation, and then numerically explore optimal pulse-sequence parameters for a realistic situation. We find an optimized sequence of a bichromatic optical lattice that excites more than 99% of the atoms to the 1st and 2nd excited bands within 100 $\mu$s without the harmonic trap. Our main finding is that the system permitting the Dirac point possesses a region of parameters where the excited energy bands become nearly parabolic, conducive to robust coherence and isochronicity. We also provide an appropriate data set for future experimentation, including effects of the atom-atom interaction by way of the mean-field nonlinear term.

Atomic momentum patterns with narrower intervals

We studied the atomic momentum distribution for a superposition of Bloch states spreading in the lowest band of an optical lattice after the action of the standing wave pulse. By designing the imposing pulse on this superposed state, an atomic momentum pattern appears with narrower interval between the adjacent peaks that can be far less than the double recoil momentum. The patterns with narrower interval come from the superposition of the action of the designed pulse on many Bloch states with quasi-momenta over the first Brillouin zone, where for each quasi-momentum there is an interference among several lowest bands. Our experimental result of narrow interval peaks is consistent with the theoretical simulation. The patterns of multi modes with different quasi-momenta are helpful for precise measurement and atomic manipulation.

Prospects for Precise Measurements with Echo Atom Interferometry

Echo atom interferometers have emerged as interesting alternatives to Raman interferometers for the realization of precise measurements of the gravitational acceleration g and the determination of the atomic fine structure through measurements of the atomic recoil frequency ω q . Here we review the development of different configurations of echo interferometers that are best suited to achieve these goals. We describe experiments that utilize near-resonant excitation of laser-cooled rubidium atoms by a sequence of standing wave pulses to measure ω q with a statistical uncertainty of 37 parts per billion (ppb) on a time scale of ∼50 ms and g with a statistical precision of 75 ppb. Related coherent transient techniques that have achieved the most statistically precise measurements of atomic g-factor ratios are also outlined. We discuss the reduction of prominent systematic effects in these experiments using off-resonant excitation by low-cost, high-power lasers.

Transformation of the Spatial Structure of an Optical Echo-Hologram Response by External Non-Resonant Pulses of Electromagnetic Standing Waves

It was shown that non-resonant electromagnetic standing wave pulses between exciting laser pulses during formation of a stimulated echo hologram transformed the wave front of the stimulated echo-hologram response.

Observation of diffraction phases in matter-wave scattering

We study the diffraction phase of different orders via the Dyson expansion series, for ultracold atomic gases scattered by a standing-wave pulse. As these diffraction phases are not observable in a single pulse scattering process, a temporal Talbot-Lau interferometer consisting of two standing-wave pulses is demonstrated experimentally with a Bose-Einstein condensate to explore this physical effect. The role of the diffraction phases is clearly shown by the second standing-wave pulse in the relative population of different momentum states. Our experiments demonstrate obvious effects beyond the Raman-Nath method, while agree well with our theory by including the diffraction phases. In particular, the observed asymmetry in the dependence of the relative population on the interval between two standing-wave pulses reflects the diffraction phase differences. The role of interatomic interaction in the Talbot-Lau interferometer is also discussed.

Effective preparation and collisional decay of atomic condensates in excited bands of an optical lattice

We present a method for the effective preparation of a Bose-Einstein condensate (BEC) into the excited bands of an optical lattice via a standing-wave pulse sequence. With our method, the BEC can be prepared in either a single Bloch state in a excited-band, or a coherent superposition of states in different bands. Our scheme is experimentally demonstrated by preparing a $^{87}$Rb BEC into the $d$-band and the superposition of $s$- and $d$-band states of a one-dimensional optical lattice, within a few tens of microseconds. We further measure the decay of the BEC in the $d$-band state, and carry an analytical calculation for the collisional decay of atoms in the excited-band states. Our theoretical and experimental results consist well.

A momentum filter for atomic gas

We propose and demonstrate a momentum filter for atomic gas-based on a designed Talbot–Lau interferometer. It consists of two identical optical standing-wave pulses separated by a delay equal to odd multiples of the half Talbot time. The one-dimensional momentum width along the long direction of a cigar-shaped condensate is rapidly and greatly purified to a minimum, which corresponds to the ground state energy of the confining trap in our experiment. We find good agreement between theoretical analysis and experimental results. The filter is also effective for non-condensed cold atoms and could be applied widely.

Measuring the atomic recoil frequency using a modified grating-echo atom interferometer

We describe progress toward a precise measurement of the recoil energy of an atom measured using a perturbative grating-echo atom interferometer (AI) that involves three standing-wave (sw) pulses. With this technique, a perturbing sw pulse is used to shift the phase of excited momentum states---producing a modulation in the contrast of the interference pattern. The signal exhibits narrow fringes that revive periodically at twice the two-photon recoil frequency, $2\omega_q$, as a function of the onset time of the pulse. Experiments are performed using samples of laser-cooled rubidium atoms with temperatures $\lesssim 5$ $\mu$K in a non-magnetic apparatus. We demonstrate a measurement of $\omega_q$ with a statistical uncertainty of 37 parts per $10^9$ (ppb) on a time scale of $\sim 45$ ms in 14 hours. Further statistical improvements are anticipated by extending this time scale and narrowing the signal fringe width. However, the total systematic uncertainty is estimated to be $\sim 6$ parts per $10^6$ (ppm). We describe methods of reducing these systematic errors.

Precision Measurement of Transition Matrix Elements via Light Shift Cancellation

We present a method for accurate determination of atomic transition matrix elements at the 10(-3) level. Measurements of the ac Stark (light) shift around "magic-zero" wavelengths, where the light shift vanishes, provide precise constraints on the matrix elements. We make the first measurement of the 5s - 6p matrix elements in rubidium by measuring the light shift around the 421 and 423 nm zeros through diffraction of a condensate off a sequence of standing wave pulses. In conjunction with existing theoretical and experimental data, we find 0.3235(9)ea(0) and 0.5230(8)ea(0) for the 5s - 6p(1/2) and 5s - 6p(3/2) elements, respectively, an order of magnitude more accurate than the best theoretical values. This technique can provide needed, accurate matrix elements for many atoms, including those used in atomic clocks, tests of fundamental symmetries, and quantum information.

Manipulating the momentum state of a condensate by sequences of standing-wave pulses

We analyze the effects of sequences of standing wave pulses on a Bose-Einstein condensate (BEC). Experimental observations are in good agreement with a numerical simulation based on the band structure theory in the optical lattice. We also demonstrate that a coherent control method based on such sequences of pulses is very efficient for experimentally designing specific momentum states.

Atom-interferometric studies of light scattering

We have used an echo-type atom interferometer that manipulates laser-cooled atoms in a single ground state to investigate the effect of light scattering from pulsed and continuous-wave light. The interferometer uses two off-resonant standing-wave pulses applied at times t=0 and t=T to diffract and recombine momentum states separated by 2({Dirac_h}/2{pi})k at t=2T. Matter wave interference is associated with the formation of a density grating with period {lambda}/2 in the vicinity of this echo time. The grating contrast is measured by recording the intensity of coherently backscattered light. The interferometer is perturbed by an additional pulse applied at t=2T-{delta}T or by continuous-wave background light. If the additional pulse is a standing wave, the momentum states interfering at t=2T are displaced and the grating contrast can be completely recovered due to constructive interference. In this case, the contrast shows a periodic modulation at the atomic recoil frequency as a function of {delta}T. In a recent work, it was shown that the atomic recoil frequency can be measured easily and precisely when using coherence functions to model the signal shape. This paper provides an alternative description of the signal shape through an analytical calculation of echo formation in the presence of an additionalmore » standing-wave pulse. Using this treatment, it is possible to model the effects of spontaneous emission and spatial profile of the laser beam on the signal shape. Additionally, the theory predicts scaling laws as a function of the pulse area and the number of additional standing-wave pulses. These scaling laws are investigated experimentally and can be exploited to improve precision measurements of the atomic recoil frequency. We also show that coherence functions can be used to make a direct measurement of the populations of momentum states associated with the ground state under conditions where the Doppler-broadened velocity distribution of the sample is much larger than the recoil velocity. These measurements are consistent with Monte Carlo wave-function simulations. If the additional pulse is a traveling wave, we find that the grating contrast measured as a function of {delta}T can be modeled by a quasiperiodic coherence function as in previous experiments that utilized atomic beams. In this work, we investigate the dependence of the photon scattering rate on the intensity and detuning of the traveling wave. We also study the effects of perturbing the interferometer with continuous-wave light and find that the dependence of the photon scattering rate on the intensity and detuning of the perturbing field is consistent with expectations.« less

Technique for measuring atomic recoil frequency using coherence functions

We have developed a technique for measuring the atomic recoil frequency using a single-state echo-type atom interferometer that manipulates laser-cooled atoms in the ground state. The interferometer relies on momentum-state interference due to two standing-wave pulses that produce density gratings. The interference is modified by applying a third standing-wave pulse during the interferometer pulse sequence. As a result, the grating contrast exhibits periodic revivals at the atomic recoil frequency ${\ensuremath{\omega}}_{r}$ as a function of the time at which the third pulse is applied, allowing ${\ensuremath{\omega}}_{r}$ to be measured easily and precisely. The contrast is accurately described by a coherence function, which is the Fourier transform of the momentum distribution, produced by the third pulse and by the theory of echo formation. If the third pulse is a traveling wave, loss of grating contrast is observed, an effect also described by a coherence function. The decay of the grating contrast as a function of continuous-wave light intensity is used to infer the cross section for photon absorption.

Influence of spontaneous emission on a single-state atom interferometer

We have studied the effects of spontaneous emission (SE) on a single-state time domain atom interferometer (AI) that uses trapped Rb atoms. The AI uses two standing wave pulses separated by time $T$ to produce an echo signal at time $2T$ due to interference between momentum states. We find that SE influences both the shape of the echo signal and its periodic time-dependent amplitude in a manner consistent with theoretical predictions. The results show that the time-dependent signal from the AI is related to the effective radiative decay rate of the excited state. We also present results that test theoretical predictions for several properties of the echo formation such as the variation in momentum transfer due to the change in the angle between the traveling wave components of the excitation pulses, strength of the atom-field interaction, and the effect of spatial profile of the excitation beams. These studies are important for realizing precision measurements of the atomic fine structure constant and gravity using this interferometer.

A scheme for the implementation of unconventional geometric phase gates with trapped ions

We propose a scheme for the realization of unconventional geometric two-qubit phase gates with two identical two-level ions. In the present scheme, the two ions are simultaneously illuminated by a standing-wave laser pulse with its pulse frequency being tuned to the ionic transition. The gate operation time can be much shorter, making the system robust against decoherence. In addition, we choose the appropriate experimental parameters to construct the geometric phase gate in one step, and thus avoid implementing the pure geometric single qubit operation.

Time domain de Broglie wave interferometry along a magnetic guide

Time domain deBroglie wave interferometry [Cahn et al, Phys. Rev. Lett. 79, 784] is applied to Rb87 atoms in a magnetic guide. A standing wave light field is carefully aligned along the guiding direction of the magnetic trapping potential from a soft-ferromagnetic 4-foil structure. A sequence of two standing wave pulses is applied to the magnetically trapped atoms. The backscattered light at the atomic density grating revival time is collected and detected via a heterodyning technique. In addition to the observed recoil oscillations that fit the interferometer theory for atoms in free space, we observe a decay of the interferometer contrast on a millisecond time scale with unexpected millisecond-scale oscillations. We find that the oscillating decay is explained by a residual variation of the linear trapping potential along the standing wave direction.

Bidirectional propagation of cold atoms in a “stadium”-shaped magnetic guide

We demonstrate the bidirectional propagation of more than ${10}^{7}\phantom{\rule{0.3em}{0ex}}\mathrm{atoms}$ ${(}^{87}\mathrm{Rb})$ around a ``stadium''-shaped magnetic ring that encloses an area of $10.9\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{2}$, with a flux density exceeding ${10}^{11}\phantom{\rule{0.3em}{0ex}}\text{atom}\phantom{\rule{0.2em}{0ex}}{\text{s}}^{\ensuremath{-}1}\phantom{\rule{0.2em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$. Atoms are loaded into the guide from a two-dimensional (and higher) magneto-optical trap at one side of the ``stadium.'' An optical standing wave pulse is applied to increase the propagation velocity of atoms along the waveguide. The atom sample fills the entire ring in $200\phantom{\rule{0.3em}{0ex}}\mathrm{ms}$ when counterpropagating atom sections of the original atom cloud recombine at their initial positions after a full revolution.

High-speed generation of macroscopic quantum-interference states for the motion of a trapped ion

A scheme is presented for the generation of macroscopic quantum-interference states for the motion of a trapped ion. In the scheme the ion is driven by a standing-wave laser beam whose carrier frequency is tuned to the ion transition. The distinct feature of the scheme is that the time required to generate the desired state is limited only by the available laser intensity, not by inherent mechanisms such as off-resonant excitations. Therefore, our scheme may allow the generation of the desired state at a high speed, which is important in view of decoherence. In the two-dimension case, entangled coherent states can be obtained. The scheme can also be used to generate entangled states for multiple modes of N trapped ions with a single strong standing-wave laser pulse.

Theory of a compound large-angle atom beam splitter

A theory of an atom beam splitter is developed involving the interaction of standing-wave field pulses with {lambda}-type atoms. The beam splitter consists of two interaction zones, both treated in the Raman-Nath approximation. There is an initial, off-resonant field (or fields) that prepares the initial atomic state, followed by interaction with a pair of standing-wave field pulses. Using this configuration one is able to create a large-angle beam splitter with a significant suppression of unwanted momentum components. The roles of relaxation and a frequency chirp are investigated, as are initial conditions for which both ground states of the {lambda} scheme are prepared by the first field. It is shown that the scheme is rather robust against fluctuations of system parameters.

Contrast interferometry using Bose-Einstein condensates to measure h/m and alpha.

The kinetic energy of an atom recoiling due to absorption of a photon was measured as a frequency, using an interferometric technique called "contrast interferometry." Optical standing wave pulses were used to create a symmetric three-path interferometer with a Bose-Einstein condensate. Its recoil phase, measurable with a single shot, varies quadratically with additional recoils and is insensitive to errors from vibrations and ac Stark shifts. We have measured the photon recoil frequency of sodium to 7 ppm precision, using a simple realization of this scheme. Plausible extensions should yield sufficient precision to attain a ppb-level determination of h/m and the fine structure constant alpha.