Recoil Limit Research Articles

A novel detection system for laser cooling of ortho-positronium

We report on the development of a position-sensitive scintillation detector system for viewing laser-cooled ortho-positronium (oPs) annihilation points. Ortho-positronium can be cooled down to a recoil limit of 0.1 K by an ultraviolet laser in spite of its relatively short lifetime. In order to perform this experiment the wavelength of Cr:LiSAF laser is considered to be 243 nm which corresponds to the transition energy of 1S–2P states of oPs. Thermal positronium plays an important role in laser cooling of oPs. We investigated various kinds and sizes of inorganic scintillators . Position resolutions of YAP:Ce and CsI(Tl), respectively, were determined to be 3.00 and 3.8 mm. Extensive Monte Carlo simulation studies were performed to view the decay positions of oPs using the time-of-flight method. Related issues of position resolution measurements and oPs decaying points will be discussed.

Heavy quark symmetry in B→D(∗)ℓν̄ spectra

Abstract We calculate heavy quark symmetry breaking in the slopes and curvatures of the B→D (∗) l ν spectra at zero recoil, including the order αs2β0 corrections. We point out that the theoretical uncertainties in the differences between B→D and B→D ∗ slopes and curvatures are smaller than in the deviations of the slopes and curvatures themselves from their infinite mass limits. We find that the central values of the current experimental results for the difference of the slopes differ from our calculations when QCD sum rules are used to estimate subleading Isgur–Wise functions. A better understanding of the shapes of the B→D (∗) l ν spectra may also help to reduce the error of |Vcb| extracted from the zero recoil limit of B→D ∗ l ν . We argue that heavy quark symmetry requires that the same fitting procedure be used in the experimental determinations of the shape parameters and |Vcb| from the B→Dl ν and B→D ∗ l ν spectra.

Doppler cooling and trapping on forbidden transitions.

Ultracold atoms at temperatures close to the recoil limit have been achieved by extending Doppler cooling to forbidden transitions. A cloud of (40)Ca atoms has been cooled and trapped to a temperature as low as 6 microK by operating a magnetooptical trap on the spin-forbidden intercombination transition. Quenching the long-lived excited state with an additional laser enhanced the scattering rate by a factor of 15, while a high selectivity in velocity was preserved. With this method, more than 10% of precooled atoms from a standard magnetooptical trap have been transferred to the ultracold trap. Monte Carlo simulations of the cooling process are in good agreement with the experiments.

Photodissociation of polarized diatomic molecules in the axial recoil limit: Control of atomic polarization

A quantum mechanical treatment of the photofragment angular momentum polarization following photodissociation of diatomic molecules is presented. This treatment extends that of Siebbeles et al. [J. Chem. Phys. 100, 3610 (1994)] by considering photodissociation of a molecule whose angular momentum is polarized in the laboratory frame, and also treats properly the angular momentum coupling between the two photofragments. The formalism treats coherent excitation of dissociative surfaces and the consequences of nonadiabatic coupling between surfaces. The possibility of exploiting the parent molecule polarization in order to control the photofragment polarization when both parallel- and perpendicular-type dissociations are active is discussed. An example is given in which significant control over the molecular frame polarization of the fragments is achieved following photolysis of a parent molecule prepared by an electric dipole transition, which may be of use in the study of photoinitiated bimolecular reactions.

Effects of asymptotic interactions on the photodissociation of HCl

Theoretical analysis is presented on the influence of the interactions among the asymptotically degenerate states correlating with Cl (2P) on the photodissociation of HCl. The spin–orbit branching ratios of Cl(2Pj, j=1/2, 3/2) are computed for low photon energy (50 000–110 000 cm−1). We predict that the branching ratios are very different from the high energy recoil limit in this energy regime and may even be inverted, due to the large influence of the interactions in the recoupling region. The angular distributions of Cl(2Pj, j=1/2, 3/2) and the alignment parameter of Cl(2P3/2) are also treated. We show that these vector properties can be significantly different from those resulting from perpendicular A 1Π–X 1Σ+ transition, indicating the role of the ground X 1Σ+ state as the dissociation channel interacting with the A 1Π state.

Experimental Investigation of Nonergodic Effects in Subrecoil Laser Cooling

We present the first detailed investigation of the line shape of the momentum distribution of atoms cooled far below the recoil limit. This distribution is deduced from a direct measurement of the atomic spatial correlation function of metastable helium atoms cooled by velocity-selective coherent population trapping. The measured line shape is then compared to the prediction of an analytical model of this cooling based on Levy statistics. A very good agreement is found between experiment and theory and fundamental features such as self-similarity and nonergodicity are identified.

Narrow-line Doppler cooling of strontium to the recoil limit

Experimental results on narrow line cooling of strontium atoms are presented. Doppler cooling is performed on the /sup 1/S/sub 0/-/sup 3/P/sub 1/ intercombination transition at 689 nm resulting in temperatures near the recoil limit in a one-dimensional (1-D) optical molasses. Frequency chirp cooling is successfully demonstrated as a means of expanding the cooling range.

B → Dlν form factors and the determination of | V cb|

The zero recoil limit of the B → Dlν form factors is calculated on the lattice, which provides a model-independent determination of | V cb |. Considering a ratio of form factors, in which the bulk of statistical and systematic errors cancel, we obtain a precise result both for h +(1) and for h −(1).

Velocity-selective coherent population trapping in caesium ions

The extension to high angular momentum transitions of laser cooling below the recoil limit based on velocity–selective coherent population trapping (VSCPT) is explored. An efficient VSCPT can be realized only by applying a compensation of the kinetic energy mismatch between the components of the superposition wavefunction and introducing repumping on the hyperfine transitions. Theoretical and experimental progress for VSCPT on cesium atoms is discussed.

Temperatures near the recoil limit in an atomic funnel

We report on an improved atomic funnel with transverse velocities near the recoil limit. Its central element is an atomic funnel, strongly tilted against the initial atomic beam axis, deflecting, compressing and cooling a laser decelerated metastable neon beam. In spite of a strong magnetic field gradient at 350 G/cm polarisation gradient cooling in the final section of the funnel leads to transverse temperatures far below the Doppler limit. These results were achieved for unusual small laser detunings, which cannot be explained by standard sub-Doppler theory.

Effects of the interactions between dissociative states and control of the product branching ratios in predissociation

The influence of the interactions between the dissociative states on the product branching ratios in predissociation is theoretically analyzed. We adopt the OH molecule as a model system and treat indirect dissociation processes with quantum interferences from the direct dissociation pathways eliminated. Various hypothetical coupling schemes between the bound electronic state and the dissociative states, and those among the dissociative states are employed. When a single dissociative state is involved in the dissociation with no interactions among the asymptotically degenerate states, recoil limit branching ratios of the triplet oxygen fine structure components O(3Pj, j=0,1,2) are attained at all energies. When a dissociative state, coupled with the bound state, is allowed to interact with other dissociative states correlating to the same atomic term, the product branching ratios approach recoil limit values only at a high energy limit. Predissociation through more than one dissociative state, interacting with each other, results in branching ratios that highly depend on the vibrational and angular momentum quantum numbers of the bound electronic state at energies below the dissociation limit to O(1D). Above the threshold to O(1D), the interactions between the dissociation channels give rise to highly oscillating branching ratios as a function of excitation energy. These findings are discussed in connection with the recent experiment of Gordon and co-workers [J. Chem. Phys. 103, 6811 (1995)] on the spin–orbit control in the predissociation of HCl.

Perturbative corrections to zero recoil inclusive B decay sum rules

Comparing the result of inserting a complete set of physical states in a time ordered product of b decay currents with the operator product expansion gives a class of zero recoil sum rules. They sum over physical states with excitation energies less than Δ, where Δ is much greater than the QCD scale and much less than the heavy charm and bottom quark masses. These sum rules have been used to derive an upper bound on the zero recoil limit of the B → D ∗ form-factor, and on the matrix element of the kinetic energy operator between B meson states. Perturbative corrections to the sum rules of order α s ( Δ) Δ 2 m c,b 2 have previously been computed. We calculate the corrections of order α s ( Δ) and α s 2( Δ) β 0 keeping all orders in Δ m c,b , and show that these perturbative QCD corrections suppressed by powers of Δ m c,b significantly weaken the upper bound on the zero recoil B → D ∗ form-factor, and also on the kinetic energy operator's matrix element.

Modifications to the chaotic dynamics of laser-cooled atoms due to spontaneous emission.

We study the dynamics of laser-cooled two-level atoms in a time-dependent standing wave. In the absence of spontaneous emission, our model reduces to the much studied quantum standard mapping. For a sample of atoms initially cooled to the Doppler limit, the momentum variance increases linearly with interaction time. A sample of atoms initially cooled to the recoil limit will display momentum diffusion at a rate that is determined by two numbers: the classical chaos parameter and a dimensionless Planck parameter. This diffusion ceases after the quantum-mechanical break time. Spontaneous emission will modify the diffusion rate of both Doppler- and recoil-cooled atoms. We show that one component of the new diffusion constant is due to spontaneous recoil and that there is a correction to the deterministic diffusion rate due to the destruction of correlations in the stroboscopic position. Spontaneous emission will destroy the dynamic localization of atoms cooled to the recoil limit. The new momentum diffusion constant can be related to the quasistationary state-decoherence rate.

Experimenters Cool Helium Below Single‐Photon Recoil Limit in Three Dimensions

A group at the Ecole Normale Superieure in Paris has placed a helium atom in a state that is going in six directions at once—a very confusing state for an atom. In such a superposition state, also called a dark state, the atom can't absorb light because the absorption amplitudes cancel out by destructive interference. The temperature corresponding to the velocity spread of each of the six wavepackets is a factor of 20 below the so‐called recoil limit for laser‐cooled atoms. The three‐dimensional subrecoil experiment in helium was reported in the 4 December issue of Physical Review Letters by John La wall (now at the National Institute of Standards and Technology in Gaithersburg, Maryland), Si‐mone Kulin, Bruno Saubamea, Nick Bigelow, Michèle Leduc and Claude Cohen‐Tannoudji.

Quantum jump calculations of velocity-selective coherent population trapping in one and two dimensions

Velocity-selective coherent population trapping is a technique for laser-cooling atoms to below the recoil limit where the momenta of the atoms and photons in the light field are equal. We have studied this mechanism using an efficient simulation model, which both simplifies the calculations and gives a physical insight into the dynamics of the anomalous diffusion process. Our calculations have been carried out for transitions in which the total atomic angular momentum is F=1 to 1 in both one and two dimensions and F=2 to 2 in one dimension. In the latter case, no exact dark state exists, and the momentum distribution tends towards a Lorentzian in the steady state.

Cooling of atoms in external fields.

We present a cooling scheme based on interactions between atoms in different internal states and on energy shifts produced by external fields. The scheme predicts temperatures below the photon recoil limit without atomic losses. It can be considered as an alternative route to reach the conditions for Bose-Einstein condensation.

New method for determining ||Vub||/||Vts|| by the processes B-bar--> rho l nu -bar and B-bar-->K*ll-bar.

The differential decay width of the process $\bar{B} \rightarrow \rho l \bar{\nu}$ is related to that of the process $\bar{B} \rightarrow K^* l \lbar$ by using $SU(3)$-flavor symmetry and the heavy quark symmetry. The ratio of the Kobayashi-Maskawa matrix elements is obtained in the zero recoil limit of $\rho$ and $K^*$, allowing a determination of $|V_{ub}|$.

Recoil-induced resonances in pump-probe spectroscopy.

When a pump field and probe field simultaneously drive an electronic-state atomic transition, the probe field absorption spectrum can consist of an absorption peak centered near \ensuremath{\Delta}'=0 and amplification peak centered near \ensuremath{\Delta}'=2\ensuremath{\Delta} (\ensuremath{\Delta} and \ensuremath{\Delta}' are the pump and probe field detunings from the atomic transition frequency, respectively). This type of spectrum is seen in the limit \ensuremath{\Vert}\ensuremath{\Delta}\ensuremath{\Vert}\ensuremath{\gg}\ensuremath{\chi}\ensuremath{\gg}\ensuremath{\Gamma}, where \ensuremath{\chi} is the Rabi frequency associated with the pump field and 2\ensuremath{\Gamma} is the homogeneous width associated with the atomic transition. For atoms cooled below the recoil limit of laser cooling, the qualitative nature of the probe absorption spectrum can undergo a dramatic change. Provided that the recoil splitting ${\mathrm{\ensuremath{\omega}}}_{\mathit{k}}$ is larger than the homogeneous decay rate (as might occur in the case of a forbidden transition), the absorption and amplification features each split into an absorption-amplification doublet. In addition, structure is found in the probe absorption spectrum near \ensuremath{\Delta}'=\ensuremath{\Delta}; this structure consists of two absorption-amplification doublets. Both doublets can be resolved if ${\mathrm{\ensuremath{\omega}}}_{\mathit{k}}$>\ensuremath{\Gamma}. If ${\mathrm{\ensuremath{\omega}}}_{\mathit{k}}$, one of the doublets can be resolved provided that ${\mathrm{\ensuremath{\omega}}}_{\mathit{k}}$>${\mathrm{\ensuremath{\Gamma}}}_{\mathit{A}}$, where ${\mathrm{\ensuremath{\Gamma}}}_{\mathit{A}}$ is some effective atomic ground state width in the problem. The positions, widths, and relative weights of all the components are readily predicted using a dressed-atom theory in which quantization of the center-of-mass momentum is included. An analytical expression for the probe field spectrum is obtained for a simple case in which spontaneous decay to the lower level is neglected. Validity criteria for the results are discussed.

Semileptonic Bc decay within heavy quark spin symmetry

We calculate the semileptonic B c decay widths using heavy quark spin symmetry. The form factors are estimated from the wave function model of Isgur, Scora, Grinstein and Wise (ISGW). We also discuss the extraction of | V cs |/| V cb |, | V cs |/| V cd | and | V ub |/| V cs | from semileptonic B c decays. The theoretical uncertainties are minimized when using the ratios of B c differential decay rates to extract the ratios of CKM elements at zero recoil limit. The result is potentially important for extracting CKM elements from future measurements at LHC and SSC.

Polarization spectra of excited-state-Mg(3p)-rare-gas-atom optical collisions.

Experimental, polarization-dependent excitation spectra for excited-state-Mg--rare-gas-atom optical collisions are reported. In these first studies of the process, polarized Mg atoms in the 3p $^{1}$${\mathit{P}}_{1}$ level are produced by absorption of linearly polarized light tuned to the 3s $^{1}$${\mathit{S}}_{0}$\ensuremath{\rightarrow}3p $^{1}$${\mathit{P}}_{1}$ resonance transition at 285.2 nm. Detuning-dependent, collision-induced polarization spectra are measured in a \ifmmode\pm\else\textpm\fi{}200-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ range around the Mg 3p $^{1}$${\mathit{P}}_{1}$\ensuremath{\rightarrow}5s $^{1}$${\mathit{S}}_{0}$ transition at 571.2 nm. The spectra correspond to probing transient Mg-Ne and Mg-Ar molecules on 3p $^{1}\mathrm{\ensuremath{\Pi}}_{1}$\ensuremath{\rightarrow}5s $^{1}\mathrm{\ensuremath{\Sigma}}_{0}^{+}$ and 3p $^{1}\mathrm{\ensuremath{\Sigma}}_{0}^{+}$\ensuremath{\rightarrow}5s $^{1}\mathrm{\ensuremath{\Sigma}}_{0}^{+}$ electronic transitions. Measurements of these excited-state polarization spectra for Mg-Ne optical collisions reveal that for detunings to the red of the atomic Mg 3p $^{1}$${\mathit{P}}_{1}$\ensuremath{\rightarrow}5s $^{1}$${\mathit{S}}_{0}$ transition, electronic linear polarization greater than 50% survives far into the molecular regime. This represents a direct measure of the polarization important to alignment-dependent inelastic processes in alkaline-earth-metal--rare-gas-atom collisions. The polarization spectra are discussed in terms of existing information on the interatomic potentials and through an axial recoil limit for the polarization degree for parallel and perpendicular molecular transitions. Rate coefficients k for disalignment of Mg 3p $^{1}$${\mathit{P}}_{1}$ atoms by collisions with Ar [k=9.4(5)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}10}$ ${\mathrm{cm}}^{3}$/s] and with Ne [k=6.5(7)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}10}$ ${\mathrm{cm}}^{3}$/s] are also extracted from the data.