Abstracts


Abstract#1

Observation of Optical Free Induction Decay in Trapped 85Rb Atoms.

S.B.CAHN, A. KUMARAKRISHNAN, U. SHIM, Y. QIU, I. BARKAN, T. SLEATOR.

We have observed Optical Free Induction Decay (FID) from 85Rb atoms confined in a magneto-optical trap. An optical pulse, 20 ns in duration was applied close to resonance with the 5S1/2 F=3 - 5P3/2 F = 4' transition, which has a lifetime of 27 ns. The FID signal was observed on a high speed photodiode using a heterodyne technique that utilizes an optical local oscillator tuned 200MHz from the excitation pulse. For comparison, absorption spectra were obtained by scanning a weak probe through the cold atoms. Before these measurements were performed, the trapping laser light and magnetic field gradient were turned off, and a small homogeneous magnetic field was turned on. Data were taken for various trap field gradients, pulse intensities and detunings. The bandwidths of the FID's (8-14 MHz, corresponding to FID decay times of 40-23 ns) were larger than the linewidths of the absorption peak under equivalent experimental conditions. In addition, the decay time of the FID amplitude was found to be larger for atoms trapped at lower field gradients. We have not determined the reason for these results but are investigating the role of collective effects.


Abstract#2

Magnetic Grating Echo (MGE) from Room Temperature Rb Atoms

A. Kumarakrishnan, S. B. Cahn, U. Shim, and T. Sleator

The application of two successive standing wave pulses results in the production and rephasing (MGE), respectively of a spatially modulated magnetic sub level coherence grating. The MGE can be used to measure velocity distributions and collision cross sections.

We have initiated a new class of coherent transient experiments with Doppler broadened atoms confined in a vapor cell following proposals in recently published work [1-3]. A spatially modulated coherence is created between magnetic sublevels of the F=3 ground state of 85Rb by a "standing wave" pulse. This pulse consists of two opposite circularly polarized traveling waves with wave vectors k1 and k2 at a small angle ø. The coherence grating is probed by the application of a "readout" pulse along k2. The resulting coherent emission along k1 is detected by a heterodyne technique. The decay of the coherence grating due to atomic motion occurs on a time scale (Kuø)-1 where u is the most probable speed of the atoms in the sample. The application of a second standing wave pulse at a time T after the first pulse causes the ground state coherence to rephase after an equal time interval T (MGE). A schematic of the experiment, an energy level diagram and the pulse sequence are shown in Figure 1(a-c).

Figure 1a : Schematic of Experiment
LO - cw optical local oscillator
BS - Beam splitter; M - Mirror; PD - Photo diode

Figure 1b : Energy Level Diagram

Figure 1c : MGE Pulse Sequence

The duration of the echo allows a determination of the velocity distribution of the atoms. Measured results show that the echo duration is proportional to (ø)-1 and that it is consistent with expectations for a vapor at room temperature. In addition, our studies show that this duration is nearly the same as the decay time of the grating after the application of the first standing wave pulse.

The lifetime of the ground state coherence (the time delay between standing wave pulses at which the echo amplitude decreases by a factor of two) is not limited by the excited state lifetime (27 ns). In principle, the time scale over which the rephasing occurs should be related to the traversal time of atoms through the region of interaction (5-10µs). However, the measured echo lifetime (~ 1µs) was found to be much shorter. Possible explanations for this discrepancy will be discussed.

The relatively long lived coherence makes the MGE a highly sensitive probe of velocity changing collisions and the presence of magnetic fields. The extension of this experiment to the case when ø=¼ may allow the measurement of inertial forces such as g, the acceleration due to gravity. When extended to trapped atoms, high precision measurements of g may be possible.

References

[1] B. Dubetsky, P. R. Berman, and T. Sleator, Phys.Rev. A 46, R2213 (1992).
[2] B. Dubetsky, P. R. Berman, Applied Physics B 59, 147 (1994).
[3] B. Dubetsky and P. R. Berman, Laser Physics, 4, 1017 (1994).


Abstract#3

Observation of Magnetic Grating Free Induction Decay (MGFID) and Magnetic Grating Echo (MGE) from Trapped Atoms.

S. B. Cahn, A. Kumarakrishnan, U. Shim and T. Sleator.
Department of Physics, New York University, New York NY 10003.

A spatially modulated magnetic sublevel coherence is induced in the F=3 ground state of 85Rb by a standing wave pulse. This pulse consists of two opposite circularly polarized travelling waves with wave vectors k1 and k2. The ground state coherence grating (MGFID) is probed at a later time by a "readout" pulse along k2. The resulting coherent emission along k1 is detected by a heterodyne technique. The application of a second standing wave pulse at a time T after the first standing wave pulse results in the rephasing of the grating at time 2T after the first pulse (MGE). We compare data from trapped atoms to data from a room temperature vapor cell.


Abstract#4

Optical Nutation in Trapped 85Rb Atoms

U. Shim, A. Kumarakrishnan, S. B. Cahn, and T. Sleator.
Department of Physics, New York University, New York NY 10003.

We investigated optical Nutation from 85Rb atoms trapped in a MOT (Magneto-Optical trap). A 500ns optical probe pulse with circular or linear polarization was tuned to the 5S1/2 F =3 - 5P3/2 F =4' transition. Before the probe pulse, a circularly polarized optical pumping pulse was applied on the the same transition as the probe pulse to make two level system. Optical Nutation was observed by a balanced detection system with two high speed photodiodes. We studied the shape and frequency of Nutation as a function of intensity and detuning. Rabi oscillation frequency and transition probability could be measured. Optical Nutation between this two level system was compared with Nutation from multilevel system containing equally populated degenerate magnetic substates. We also studied steady state value after Nutation was damped. Experimental data gave us a good agreement with theoretical prediction.


Abstract#5

Sub-Doppler Temperature Measurements of Trapped 85Rb Using Magnetic Grating Free Induction Decay and Echo Techniques

A. Kumarakrishnan, S. B. Cahn, U. Shim and T. Sleator.
Department of Physics, New York University, New York NY 10003.

The production and rephasing of a ground-state magnetic sublevel coherence grating results in two transient signals, the Magnetic Grating Free Induction Decay (MGFID) and the Magnetic Grating Echo (MGE), respectively. The gratings are produced and rephased by the application of two sets of simultaneous + - - traveling wave laser pulses 40 to 80 MHz off resonance with the 85Rb F=3 F=4' transition, where the pulses' k-vectors are either directed at a small angle ø (Forward), or nearly opposite (Backward). We have measured sub-Doppler temperatures of atoms in a magneto-optical trap from the duration of these signals. Results are compared with theory and time-of-flight measurements.1 The MGE lifetime, defined as the time between pulses at which the amplitude of the signal is half its maximum, is shorter than the expected value (the time the atoms remain in the interaction region). We discuss this discrepancy and the potential application of the Backward MGE to a precision measurement of g .

1C. D. Wallace et al. JOSAB, 11, 703, (1994).


Abstract#6

Interferometric Measurement of Atomic Recoil Frequency Using Pulsed Optical Standing Waves on a MOT-Cooled 85Rb Vapor

S. B. Cahn, A. Kumarakrishnan, U. Shim and T. Sleator.
Department of Physics, New York University, New York NY 10003.

We have established a population grating in a MOT-cooled 85Rb vapor and observed the scattering of a laser pulse from it. The grating is produced by the action of two ~ 100 ns + off-resonance standing waves, separated by a time T, where T is as large as 2 ms. The first laser pulse causes a phase modulation of the atomic wavefunction, which evolves into a population grating before dephasing. This grating is rephased by the second pulse, and the population grating reappears just before and after times t = 2T, 3T, 4T . The magnitude of the scattered signal is periodic in T, with a frequency r = ( k)2/m. This frequency r is the signature of the discrete recoil of the atom due to photon absorption. We have measured the frequency for oppositely directed, k = 2k, and perpendicular, k = 21/2k, traveling wave components of the two standing waves and inferred values for that are consistent to 1 part in 10000 with the currently accepted value. We determined the acceleration due to gravity, g, by measuring the phase of the signal as a function of T.


Abstract#7

Effects of Magnetic Fields on Magnetic Grating Free Induction Decay (MGFID) in a Cold Rb Vapor

S. B. Cahn, A. Kumarakrishnan, U. Shim and T. Sleator.
Department of Physics, New York University, New York NY 10003.

We have created and detected a magnetic sublevel coherence in trapped Rb atoms by applying a pair of short pulses of opposite circularly polarized light fields, both co- and counterpropagating. The effects of magnetic fields were measured and modeled. As presented in another paper at this conference, the Magnetic Grating Free Induction Decay (MGFID) may be produced in a sample of room temperature (300 K) 85Rb, demonstrating the coherence between alternate magnetic sublevels m = 2. The decay rate of this coherence is dominated by the dispersal of the atoms and proportional to the most probable velocity u of the atoms. By slowing and confining the atoms in a magneto-optic trap, the decay rate may be reduced by several orders of magnitude, and effects due to weak magnetic fields may be investigated. The optical pulses of + and - light were applied close to resonance with the 85Rb 3 4' transition at a small angle ø between their k vectors , k1 and k2, respectively. The coherence produced decays at a rate kuø, where k=2¼/ and =780nm. Since the coherence is between ground state sublevels, it does not produce radiation, so a signal is produced by the subsequent application of a + "readout" pulse applied along k2. This light is scattered by the coherence grating into k1 with the opposite - polarization. Measurements of the decay time ~ 100µs yielded a temperature of ~ 0.7mK. Performing the experiment with counterpropagating pulses produced a decay time of ~ 200ns and a temperature of ~ 0.5mK. The signal was detected using an optical heterodyne technique, and further mixed down using an RF homodyne technique with two RF local oscillators ¼/2 apart in phase. By applying a magnetic field nearly parallel to the direction of propagation of the two travelling wave light pulses that produced the ground state coherence, the phase evolution of alternate ( m =2) magnetic sublevels was observed. The measured dependence of the frequency of oscillation on applied magnetic field (see Figure 1) gave excellent agreement with theory (2/3 µB). The application of a magnetic field perpendicular to the direction of propagation of the light pulses gave oscillations of the magnitude of the signal with 100% visibility (see Figure 2), as expected from an analytic solution for the evolution of the coherence in the presence of a magnetic field. As a field parallel to the k vectors was added, the frequency of oscillation increased, and the amplitude and visibility decreased, as expected.


Abstract#8

Atom Interferometric Measurement of Atomic Recoil Frequency Using Pulsed Optical Standing Waves on a MOT-Cooled 85Rb Vapor

S. B. Cahn, A. Kumarakrishnan, U. Shim and T. Sleator.
Department of Physics, New York University, New York NY 10003.

We report the development of an atom interferometer that uses optical standing waves as phase gratings and operates entirely in the time domain. We have used this interferometer to measure the recoil frequency of a 85Rb atom to 1 part in 104, and the acceleration due to gravity ("little g") to better than 5 parts in 104. In our interferometer, 85Rb atoms are first cooled from a room-temperature vapor by a Magneto-optical trap (MOT). After the trapping laser beams and magnetic field are turned off, two + off-resonance (~ 84 MHz detuning) standing wave pulses (~ 100 ns duration) are applied, separated by a time T, where T is as large as 2 ms. The first laser pulse imposes a phase modulation on the initial atomic wavefunction, which evolves into an amplitude modulation (representing an atomic population grating) while the system dephases. This dephasing is due to the non-zero velocity spread of the laser-cooled cloud. After the second pulse, the atomic population grating reappears just before and after times t = 2T, 3T, 4T, ... from the first pulse. We observe this rephased population grating by scattering an off-resonant traveling wave from it, and measuring the (complex) amplitude of the scattered light field using a heterodyne technique.

We find that the magnitude of the scattered signal is periodic in T, with a frequency = 2 k, where k ( k)2/2 m, and k |k2 - k1| is the difference in wave vectors of the fields comprising the standing wave (|k1| = |k2| = k). This frequency k is the signature of the discrete recoil of the atom due to photon absorption and re-emission. We have measured k for oppositely directed, k = 2k, and perpendicular, k = 21/2k, traveling wave components of the two standing waves and inferred values for that are consistent to 1 part in 10000 with the currently accepted value. In addition to being periodic in T, the signal almost entirely disappears for T = n ¼/ k (n an integer), implying a fringe "visibility" of close to 100%.

We have also determined the acceleration due to gravity, g, by measuring the phase of the back-scattered signal as a function of T for a vertically aligned standing wave. We find that the phase is well modeled by ø(T) = 2kgT2 with a value of g = 9.798 m/s2 (Greenwich Village, New York).


Abstract#9

Observations Of Long Lived Coherent Transients From Trapped Atoms And Doppler Broadened Vapor

A. Kumarakrishnan, S. B. Cahn, U. Shim and Tycho Sleator.

A spatially modulated coherence is created between magnetic sublevels of the F=3 ground state in dilute laser cooled 85 Rb vapor by the application of a pair of simultaneous +- - traveling wave laser pulses. The wave vectors of these pulses are along k2 and k1, respectively, at a small angle (Forward), or nearly opposite (Backward). The decay of the coherence grating is referred to as Magnetic Grating Free Induction Decay (MGFID) [1,2] and is probed at a later time by a + polarized "readout pulse" along k2. The resulting - polarized coherent emission along k1 is detected by a heterodyne technique. The decay of the coherence is due to thermal motion and takes place on a time scale (Ku sin)-1 where u is the most probable speed of atoms in the sample. We have used the MGFID to measure very narrow velocity distributions (Ku < ), where is the natural linewidth of the F=3 F=4' transition (5.9 MHz). We have measured decay times between 100µs - 400µs for trapped atoms corresponding to a velocity spread Ku in the range 2 MHz - 0.6 MHz. We have therefore been able to infer the temperature of trapped atoms for a variety of trap laser intensities and detunings.

The application of a second pair of +- - traveling wave pulses at a time T after the first causes the ground state coherence to rephase after an equal time interval T (Magnetic Grating Echo or MGE). The duration of the MGE is -1 (for small ), and is nearly the same as the decay time of the MGFID. In cold atoms, have observed this rephasing for up to 4 ms after excitation by the first set of pulses. The MGE lifetime, defined as the time between pulses at which the amplitude of the signal is half its maximum, is limited only by the time the atoms remain in the interaction region. This makes the MGE a highly sensitive probe of velocity distributions and magnetic fields. In addition, the Backward MGE may allow a precision measurement of the acceleration due to gravity [3]. It is also expected that the MGE will be periodic in T with a modulation at the atomic recoil frequency K= K2/2m. This periodicity could possibly be used for a precision measurement of /m [4].

We have extended these experiments to a Doppler broadened column of room temperature Rb vapor. The durations of the MGFID and MGE are ~ 200 ns and consistent with estimates for the velocity distribution. However, the MGE lifetime (~ 2.5 µs) is shorter than the expected value (the traversal time of atoms through the region of interaction). We plan to use the MGE for accurate measurements of velocity changing ground state collision cross sections.

NYU/ GSAS/ Atomic Physics