Superchemistry: Dynamics of Coupled Atomic and Molecular Bose-Einstein Condensates
D. J. Heinzen, R. Wynar, P. D. Drummond, and K. V. Kheruntsyan
Phys. Rev. Lett. 84, 5029 (2000).
We analyze the dynamics of a dilute, trapped Bose-condensed atomic gas coupled to a diatomic molecular Bose gas by coherent Raman transitions. This system is shown to result in a new type of "superchemistry," in which giant collective oscillations between the atomic and the molecular gas can occur. The phenomenon is caused by stimulated emission of bosonic atoms or molecules into their condensate phases. (17 References).
Molecules in a Bose-Einstein Condensate
R. Wynar, R. S. Freeland, D. J. Han, C. Ryu, and D. J. Heinzen
Science 287, 1016 (2000).
State-selected rubidium-87 molecules were created at rest in a dilute Bose-Einstein condensate of rubidium-87 atoms with coherent free-bound stimulated Raman transitions. The transition rate exhibited a resonance line shape with an extremely narrow width as small as 1.5 kilohertz. The precise shape and position of the resonance are sensitive to the mean-field interactions between the molecules and the atomic condensate. As a result, we were able to measure the molecule-condensate interactions. This method allows molecular binding energies to be determined with unprecedented accuracy and is of interest as a mechanism for the generation of a molecular Bose-Einstein condensate. (24 References).
Coupled Singlet-Triplet Analysis of Two-Color Cold-Atom Photoassociation Spectra
J. M. Vogels, R. S. Freeland, C. C. Tsai, B. J. Verhaar, and D. J. Heinzen
Phys. Rev. A 61, 043407 (2000).
We describe a method that is well suited to analysis of the bound states of the alkali-metal dimers near their dissociation limit. The method combines inverse perturbation theory, coupled-channel bound-state theory, and the accumulated phase method to treat the short-range part of the molecular potentials. We apply this method to analyze the bound-state energies measured in a two-color photoassociation experiment in an ultracold 85Rb gas. This analysis yields information on the interactions between ultracold 85Rb atoms that is important to the understanding of ultracold Rb collisions and Bose-Einstein condensation. (33 References).
Time-Independent and Time-Dependent Photoassociation of Spin-Polarized Rubidium
H. M. J. M. Boesten, C. C. Tsai, D. J. Heinzen, A. J. Moonen, B. J. Verhaar
J. Phys. B 32, 287 (1999).
We extract information about collisions of ultra-cold ground-state rubidium atoms from observations of a g-wave shape resonance in the 85Rb+85Rb system via time-independent and time-dependent photoassociation. The shape resonance arises from a quasi-bound state inside a centrifugal barrier that enhances the excitation to the bound electronically excited state by the photoassociation laser in the time-independent experiment. The shape resonance is sufficiently long-lived that its build-up through the barrier can be observed by first depleting it via a photoassociation laser pulse and then measuring the rate of photoassociation by a second laser pulse with a variable delay time. A combined method of analysis of the time-independent and time dependent experiments is presented. We discuss the spectroscopy of states of two particles with spin trapped inside a centrifugal barrier. Interacting via direct and indirect spin-spin interactions. (34 References).
State-Selective Rabi and Ramsey Magnetic Resonance Line Shapes
G. Xu and D. J. Heinzen
Phys. Rev. A 59, R922 (1998).
We carry out state-selective Rabi and Ramsey magnetic-resonance experiments on ground-state 133Cs(F=4) atoms. Novel line
shapes are obtained, which exhibit very sharp features with a width much smaller than the inverse duration of the magnetic-resonance
pulse. The sensitivity of ordinary magnetic-resonance experiments with total spin F > ½ is significantly less than the Heisenberg limit,
which can be exactly realized only with maximally correlated spin states. We show that the state-selective resonances yield sensitivity very
close to the Heisenberg limit, without any state preparation beyond ordinary optical pumping. (9 References).
Observation of a Feshbach Resonance in Cold Atom Scattering
Ph. Courteille, R. S. Freeland, D. J. Heinzen, F. A. van Abeelen, and B. J. Verhaar
Phys. Rev. Lett. 81, 69 (1998).
We probe s-wave collisions of laser-cooled 85Rb(f = 2, mf = -2) atoms with Zeeman-resolved photoassociation spectroscopy. We observe that these collisions exhibit a magnetically tunable Feshbach resonance, and determine that this resonance tunes to zero energy at a magnetic field of 164 ± 7 G. This result indicates that the self-interaction energy of an 85Rb Bose-Einstein condensate can be magnetically tuned. We also demonstrate that Zeeman-resolved photoassociation spectroscopy provides a useful new tool for the study of ultracold atomic collisions. (25 References).
Bose-Einstein Condensation of Large Numbers of Atoms in a Magnetic Time-Averaged Orbiting Potential Trap
D. J. Han, R. H. Wynar, Ph. Courteille, and D. J. Heinzen
Phys. Rev. A 57, R4114 (1998).
We have observed Bose-Einstein condensation of large numbers of 87Rb atoms in a magnetic time-averaged orbiting potential (TOP) trap. Over 1.5*109 atoms are captured in the trap and evaporatively cooled to produce condensates containing up to 2*105 atoms. We discuss special considerations relating to the production of large Bose-Einstein condensates in a TOP trap, and present measurements of the condensate fraction for this case. (23 References).
Photoassociation as a Probe of Feshbach Resonances in Cold-Atom Scattering
F. A. Van Abeelen, D. J. Heinzen, and B. J. Verhaar
Phys. Rev. A 57, R4102 (1998).
We investigate theoretically the influence of magnetically tunable Feshbach collision resonances on the photoassociation spectra of ultracold atoms. As an example we consider recently predicted resonances for 85Rb atoms. For excitation to the 85Rb2 0g- (S1/2+P1/2) electronic state, we predict that the photoassociation rate is resonantly enhanced by at least two orders of magnitude. We find that photoassociation could serve as a useful probe with which to study Feshbach resonances in ultracold collisions. In turn, these resonances should be very important to Bose-condensed gases, and more generally, to coherent atom optics. (15 References).
Predictions for Laser-Cooled Rb Clocks
S. J. J. M. F. Kokkelmans, B. J Verhaar, K. Gibble, and D. J. Heinzen
Phys. Rev. A 56, R4389 (1997).
Using information from a recent 85Rb two-color photoassociation experiment, we evaluate the merits of fountain clocks based on 87Rb and 85Rb isotopes as alternatives to 133Cs and find that they offer significant advantages. In the case of 87Rb the collisionally induced fractional frequency shift is 15 times smaller than for 133Cs. This small shift is associated with a small difference in the triplet and singlet scattering lengths for 87Rb. For 85Rb, the shift produced by the two mf = 0 clock states may have opposite signs allowing the shift to be eliminated by controlling the relative populations of these states. We also present collision quantities relevant to atomic fountain clocks containing multiply launched groups of atoms, and for evaporative cooling of 85Rb atoms. (20 References).
Two-Color Photoassociation Spectroscopy of Ground State Rb2
C.C. Tsai, R.S.Freeland, J.M. Vogels, H.M.J.M. Boesten, B.J. Verhaar, and D.J. Heinzen
Phys. Rev. Lett. 79, 1245 (1997).
We determine the energies of twelve vibrational levels lying within 20 GHz of the lowest dissociation limit of 85Rb2 with two-color photoassociation spectroscopy of ultracold 85Rb atoms. The levels lie in an energy range for which singlet and triplet states are mixed by the hyperfine interaction. We carry out a coupled channels bound state analysis of the level energies, and derive accurate values for 85Rb2 interaction parameters. The information obtained is sufficient to allow for quantitative calculations of arbitrary Rb ultracold collision properties.
Prediction of Feshbach Resonances in Collisions of Ultracold Rubidium Atoms
J. M. Vogels, C. C. Tsai, S. J. J. M. F. Kokkelmans, B. J. Verhaar, and D. J. Heinzen
Phys. Rev. A 56, R1067 (1997).
Making use of continuum and bound-state data, we predict B-field induced Feshbach resonances in collisions of ultracold rubidium atoms that make it possible to control the sign and magnitude of the effective particle-particle interaction in a Bose condensate by tuning a bias magnetic field. For the case of 85Rb they occur at field values in the range where these atoms can be magnetostatically trapped. For 87Rb they are predicted to occur at negative field values.
Observation of a Shape Resonance in the Collision of Two Cold 87Rb Atoms
H. M. J. M. Boesten, C. C. Tsai, J. R. Gardner, D. J. Heinzen, and B. J. Verhaar
Phys. Rev. A 55, 636 (1997).
We observe a shape resonance in the scattering of two ultracold 87Rb atoms, causing the colliding atoms to form a long-living compound system inside an l = 2 centrifugal barrier. Its existence follows from a photoassociation experiment in a gas sample of doubly polarized 87Rb atoms. Using it we are able to carry out direct determinations of the triplet scattering length for 87Rb, relevant to Bose-Einstein condensation experiments, and of the Rb+Rb C6 dispersion coefficient. Consequences for the 85Rb scattering length are discussed. (27 References).
Optimal Frequency Measurements with Maximally Correlated States
J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen
Phys. Rev. A 54, R4649 (1996).
We show how maximally correlated states of N two-level particles can be used in spectroscopy to yield a frequency uncertainty equal to (NT)-1, where T is the time of a single measurement. From the time-energy uncertainty relation we show that this is the best precision possible. We rephrase these results in the language of particle interferometry and obtain a state and detection operator which can be used to achieve a phase uncertainty exactly equal to the 1/N Heisenberg limit, where N is the number of particles used in the measurement. (29 References).
Observation of a Shape Resonance in Cold-Atom Scattering by Pulsed Photoassociation
H. M. J. M. Boesten, C. C. Tsai, B. J. Verhaar, and D. J. Heinzen
Phys. Rev. Lett. 77, 5194 (1996).
We observe the time dependence of a cold-atom collision in a pulsed photoassociation experiment. For a g-wave shape resonance in the 85Rb + 85Rb system we measure the time needed to build up the resonant state by tunneling through the centrifugal barrier. Combining this with time-independent 85Rb and 87Rb photoassociation we determine the resonance energy and find evidence for the decay of the shape resonance into inelastic channels. We also determine the 85Rb + 85Rb and 87Rb + 87Rb C6 coefficient and triplet scattering lengths without relying on ab initio calculations. (16 References).
Collisions of Doubly Spin Polarized, Ultracold 85Rb Atoms
J. R. Gardner, R. A. Cline, J. D. Miller, D. J. Heinzen, H. M. J. M. Boesten, and B. J. Verhaar
Phys. Rev. Lett. 74, 3764-3767 (1995).
We study the collisions of doubly spin-polarized 85Rb atoms at millikelvin temperatures using photoassociation spectroscopy. Because the atoms are spin polarized, only triplet collisional states are formed. This leads to photoassociation spectra of a particularly simple form, which provide a very direct probe of the ground state collision. These spectra are analyzed to yield the ground state triplet scattering length -1000a0.
Study of Rb2 Long-Range States by High Resolution Photoassociation Spectroscopy
R. A. Cline, J. D. Miller, and D. J. Heinzen
Phys. Rev. Lett. 73, 632-635 (1994)
We study the states of Rb2 that lie within 35 cm-1 of the 52S1/2 + 52P3/2 dissociation limit with photoassociation spectroscopy of laser-cooled Rb atoms. We observe the rotationally resolved bound levels of the novel 0g- 'pure long-range' state, which has an inner turning point beyond 25 bohrs. We also identify levels belonging to 1g and 0u+ states and find that the 0u+ levels are broadened by predissociation. With our new method, excited molecular states with a binding energy from less than 0.3 to more than 1000 cm-1 can be studied with a resolution better than 0.002 cm-1.
Role of Collisions in the Search for an Electron Electric-Dipole Moment
M. Bijlsma, B. J. Verhaar, and D. J. Heinzen
Phys. Rev. A 49, R4285-R4288 (1994).
We study the role of atomic collisions in future measurements of an intrinsic electric-dipole moment (EDM) of the electron using laser-cooled Cs atoms in an optical trap or in an atomic fountain. We find that the shift in frequency and the line broadening caused by collisions may eventually limit the achievable sensitivity of these EDM experiments. We present the results of a coupled-channel calculation of these quantities and discuss the symmetry aspects and magnetic-field dependences.
Squeezed Atomic States and Projection Noise in Spectroscopy
D. J. Wineland, J. J. Bollinger, W. M. Itano, and D. J. Heinzen
Phys. Rev. A 50, 67-88 (1994).
We investigate the properties of angular-momentum states which yield high sensitivity to rotation. We discuss the application of these ``squeezed-spin'' or correlated-particle states to spectroscopy. Transitions in an ensemble of N two-level (or, equivalently, spin-½) particles are assumed to be detected by observing changes in the state populations of the particles (population spectroscopy). When the particles' states are detected with 100% efficiency, the fundamental limiting noise is projection noise, the noise associated with the quantum fluctuations in the measured populations. If the particles are first prepared in particular quantum-mechanically correlated states, we find that the signal-to-noise ratio can be improved over the case of initially uncorrelated particles. We have investigated spectroscopy for a particular case of Ramsey's separated oscillatory method where the radiation pulse lengths are short compared to the time between pulses. We introduce a squeezing parameter xR which is the ratio of the statistical uncertainty in the determination of the resonance frequency when using correlated states vs that when using uncorrelated states. More generally, this squeezing parameter quantifies the sensitivity of an angular-momentum state to rotation. Other squeezing parameters which are relevant for use in other contexts can be defined. We discuss certain states which exhibit squeezing parameters xR [approx. equal] N-½. We investigate possible experimental schemes for generation of squeezed-spin states which might be applied to the spectroscopy of trapped atomic ions. We find that applying a Jaynes-Cummings-type coupling between the ensemble of two-level systems and a suitably prepared harmonic oscillator results in correlated states with xR < 1.
Spin Relaxation of Optically Trapped Atoms by Light Scattering
R. A. Cline, J. D. Miller, M. R. Matthews, and D. J. Heinzen
Opt. Lett. 19, 207-209 (1994).
We study spin relaxation of optically trapped atoms that is due to light scattering from the trap laser. We observe relaxation times greater than 2 s for ground-state hyperfine-level populations of 85Rb atoms trapped in an optical dipole force trap operating as much as 65 nm to the red of the D1 line. The measured relaxation rate can be more than 100 times slower than the atoms' total spontaneous scatter rate from the trap laser. This enhancement in atomic ground-state lifetime is due to an interference effect in spontaneous Raman scattering far from atomic resonance.
Photoassociation Spectrum of Ultra-Cold Rb Atoms
J. D. Miller, R. A. Cline, and D. J. Heinzen
Phys. Rev. Lett. 71, 2204-2207 (1993).
The authors study the photoassociative collisional loss of laser-cooled Rb atoms from a far-off resonance optical dipole force atom trap. They obtain a well-resolved photoassociation spectrum from 50 cm-1 to 980 cm-1 below the first excited dissociation limit of the Rb2 molecule. Two vibrational series associated with excited Rb2 3Sg+ states are clearly visible. Oscillations in the associated Franck-Condon factors reflect the structure of the triplet ground state wave function. Their results clearly demonstrate the potential of photoassociation spectroscopy as a new probe of molecular structure.
Far Off-Resonance Optical Trapping of Atoms
J. D. Miller, R. A. Cline, and D. J. Heinzen
Phys. Rev. A 47, R4567-R4570 (1993).
The authors confine 85Rb atoms in an optical dipole force trap with a very large detuning from resonance of up to 65 nm. Confinement times of 200 ms, limited only by background-gas collisions, are obtained without additional cooling. A typical trap contains 1300 atoms at a temperature of 0.4 mK and a peak density of 8*1011 cm-3. The authors measure spontaneous photon scatter rates of the trapped atoms to be less than 1.6*103 s-1, corresponding to recoil heating rates below 0.6 mK/s. The far-detuned trap confines atoms with a strong, nearly conservative optical force and negligible atomic excitation.
Quantum Projection Noise: Population Fluctuations in Two-Level Systems
W. M. Itano, J. C. Bergquist, J. J. Bollinger, J. M. Gilligan, D. J. Heinzen, F. L. Moore, M. G. Raizen, and D. J. Wineland
Phys. Rev. A 47, 3554-3570 (1993).
Measurements of internal energy states of atomic ions confined in traps can be used to illustrate fundamental properties of quantum systems, because long relaxation times and observation times are available. In the experiments described here, a single ion or a few identical ions were prepared in well-defined superpositions of two internal energy eigenstates. The populations of the energy levels were then measured. For an individual ion, the outcome of the measurement is uncertain, unless the amplitude for one of the two eigenstates is zero, and is completely uncertain when the magnitudes of the two amplitudes are equal. In one experiment, a single 199Hg+ ion, confined in a linear RF trap, was prepared in various superpositions of two hyperfine states. In another experiment, groups of 9Be+ ions, ranging in size from about 5 to about 400 ions, were confined in a Penning trap and prepared in various superposition states. The measured population fluctuations were greater when the state amplitudes were equal that when one of the amplitudes was nearly zero, in agreement with the predictions of quantum mechanics. These fluctuations, which the authors call quantum projection noise, are the fundamental source of noise for population measurements with a fixed number of atoms. These fluctuations are of practical importance, since they contribute to the errors of atomic frequency standards.
Spin Squeezing and Reduced Quantum Noise in Spectroscopy
D. J. Wineland, J. J. Bollinger, W. M. Itano, F. L. Moore, and D. J. Heinzen
Phys. Rev. A 46, R6797-R6800 (1992).
The authors investigate the quantum-mechanical noise in spectroscopic experiments on ensembles of N two-level (or spin-½) systems where transitions are detected by measuring changes in state population. By preparing correlated states, here called squeezed spin states. One can increase the signal-to-noise ratio in spectroscopy (by approximately N½ in certain cases) over that found in experiments using uncorrelated states. Possible experimental demonstrations of this enhancement are discussed.
Department of Physics
University of Texas at Austin
© 1999, 2000, 2001 Ultracold Atomic Physics Group