Cavity cooling of translational and ro-vibrational motion of molecules: ab initio-based simulations for OH and NO

We present detailed calculations on the basis of our recent proposal for simultaneous cooling of the rotational, vibrational and external molecular degrees of freedom [1]. In this method, the molecular ro-vibronic states are coupled by an intense laser and an optical cavity via coherent Raman processes enhanced by the strong coupling with the cavity modes. For a prototype system, OH, we showed that the translational motion is cooled to a few μK and the molecule is brought to the internal ground state in about a second. Here, we investigate numerically the dependence of the cooling scheme on the molecular polarizability, selecting NO as a second example. Furthermore, we demonstrate the general applicability of the proposed cooling scheme to initially vibrationally and rotationally hot molecular systems. PACS 33.80.Ps; 32.80.Lg; 42.50.Pq     

Cavity QED with quantized center of mass motion

We investigate the quantum fluctuations of a single atom in a weakly driven cavity, where the center of mass motion of the atom is quantized in one dimension. We present analytic results for the second order intensity correlation function g((2))(tau) and the intensity-field correlation function h(theta)(tau), for transmitted light in the weak driving field limit. We find that the coupling of the center of mass motion to the intracavity field mode can be deleterious to nonclassical effects in photon statistics and field-intensity correlations, and compare the use of trapped atoms in a cavity to atomic beams.     

Cavity cooling of atoms: within and without a cavity

We compare the efficiencies of two optical cooling schemes, where a single particle is either inside or outside an optical cavity, under experimentally-realisable conditions. We evaluate the cooling forces using the general solution of a transfer matrix method for a moving scatterer inside a general one-dimensional system composed of immobile optical elements. Assuming the same atomic saturation parameter, we find that the two cooling schemes provide cooling forces and equilibrium temperatures of comparable magnitude.     

Blackbody-radiation-assisted laser cooling of molecular ions

The translational motion of molecular ions can be effectively cooled sympathetically to temperatures below 100 mK in ion traps through Coulomb interactions with laser-cooled atomic ions. The distribution of internal rovibrational states, however, gets in thermal equilibrium with the typically much higher temperature of the environment within tens of seconds. We consider a concept for rotational cooling of such internally hot, but translationally cold, heteronuclear diatomic molecular ions. The scheme relies on a combination of optical pumping from a few specific rotational levels into a "dark state" with redistribution of rotational populations mediated by blackbody radiation.     

Modes of internal motion in three-body systems

We propose an approach to investigate the possible internal motions of three-body quantum-mechanical systems held together by pairwise potentials. The method utilizes the shape-density functions which we define and then extract from the eigenwave functions of the system. Through these densities we determine the dominant geometric configurations and modes of internal motion of the 0⁺, 2⁺ and 4⁺ states of a model three-boson system with and without a repulsive core in the interaction.Research supported in part by NSF Grant No. PHY83-06584 and by The Science Fund of the Chinese Academy of Sciences     

Quantum theory of cavity-assisted sideband cooling of mechanical motion

We present a quantum-mechanical theory of the cooling of a cantilever coupled via radiation pressure to an illuminated optical cavity. Applying the quantum noise approach to the fluctuations of the radiation pressure force, we derive the optomechanical cooling rate and the minimum achievable phonon number. We find that reaching the quantum limit of arbitrarily small phonon numbers requires going into the good-cavity (resolved phonon sideband) regime where the cavity linewidth is much smaller than the mechanical frequency and the corresponding cavity detuning. This is in contrast to the common assumption that the mechanical frequency and the cavity detuning should be comparable to the cavity damping.     

Laser cooling of internal degrees of freedom of molecules

Optical pumping techniques using laser fields combined with photo-association of ultracold atoms leads to control of the vibrational and/or rotational population of molecules. In this study, we review the basic concepts and main steps that should be followed, including the excitation schemes and detection techniques used to achieve ro-vibrational cooling of Cs₂ molecules. We also discuss the extension of this technique to other molecules. In addition, we present a theoretical model used to support the experiment. These simulations can be widely used for the preparation of various experiments because they allow the optimization of several important experimental parameters.     

Longitudinal focusing and cooling of a molecular beam

A neutral polar molecule experiences a force in an inhomogeneous electric field. This electric field can be designed such that a beam of polar molecules is exposed to a harmonic potential in the forward direction. In this potential the longitudinal phase-space distribution of the ensemble of molecules is rotated uniformly. This property is used to longitudinally focus a pulsed beam of ammonia molecules and to produce a beam with a longitudinal velocity spread of 0.76 m/s, corresponding to a temperature of 250 mu K.     

Cavity nonlinear optics at low photon numbers from collective atomic motion

We report on Kerr nonlinearity and dispersive optical bistability of a Fabry-Perot optical resonator due to the displacement of ultracold atoms trapped within. In the driven resonator, such collective motion is induced by optical forces acting upon up to 10(5) 87Rb atoms prepared in the lowest band of a one-dimensional intracavity optical lattice. The longevity of atomic motional coherence allows for strongly nonlinear optics at extremely low cavity photon numbers, as demonstrated by the observation of both branches of optical bistability at photon numbers below unity.     

Fractal analysis of molecular motion in liquids

The fractal analysis of atomic trajectories in a simulated liquid gives Richardson coefficients, α, which depend on the duration, t, of the trajectory i.e., α(t). It is shown that α(t) can be expressed in terms of the usual self-diffusion coefficient and a parameter which is related to the details of the motion for times of order of the velocity autocorrelation time. It is shown that even when conventional diffusional behaviour is very amply obeyed it is probably impractical to show by computer simulation that the corresponding fractal result, α → 1, (D → 2), is valid without the aid of a theory such as the one presented here.     

The molecular Hamiltonian in internal coordinates

A systematic approach for the derivation of the exact translational–rovibronic (non-relativistic) Hamiltonian for a polyatomic molecule consisting of N nuclei and n electrons is presented. All coupling terms which contribute to the total energy are identified. The Hamiltonian is greatly simplified by taking the internal coordinates (bond lengths and bond angles) as the vibrational variables. The translational–rovibronic Hamiltonian of triatomic molecules are considered as an application for this general formulation.     

Sympathetic cooling of complex molecular ions to millikelvin temperatures

Gas-phase singly protonated organic molecules of mass 410 Da (Alexa Fluor 350) have been cooled from ambient temperature to the hundred millikelvin range by Coulomb interaction with laser-cooled barium ions. The molecules were generated by an electrospray ionization source, transferred to and stored in a radio-frequency trap together with the atomic ions. Observations are well described by molecular dynamics simulations, which are used to determine the spatial distribution and thermal energy of the molecules. In one example, an ensemble of 830 laser-cooled 138Ba+ ions cooled 200 molecular ions to less than 115 mK. The demonstrated technique should allow a large variety of protonated molecules to be sympathetically cooled, including molecules of much higher mass, such as proteins.     

Steady state dislocation motion via molecular dynamics

Nonequilibrium molecular dynamics is applied to the generation and steady propagation of edge dislocations. “Normal” propagation at about one-third the longitudinal sound speed, transonic propagation at nine-tenths that speed, climb, and multiplication are all observed.     

Temperature dependent J coupling and internal motion in acetaldehyde

The indirect proton spin-spin coupling (J) in acetaldehyde has been measured with an accuracy of ±0·01 c.p.s. over the temperature range -119°c to +52°c. The small change of 0·15 c.p.s. is interpreted in terms of the internal motion of the molecule which gives an average of J over its angular thermally excited motion in a three-well potential. The constant and cos 3? terms in J(?) are determined and an estimate of J(?) is made. It is pointed out that the zero point internal vibration in this and similar molecules may be important for the comparison of experimental and theoretical J values. Although J falls with increasing temperature in acetaldehyde it may well rise in other similar molecules.     

Evaporative cooling of hydrogen molecular ions in a Penning trap

Evaporative cooling of singly charged ions in a Penning trap is studied. The ions are created by in-situ electron bombardment of hydrogen molecules and trapped in a cylindrical Penning trap. Cooling of the ions is observed by their axial motion after trapping of a few hundred milliseconds. The ions temperature decreases by a factor of more than 6 in 800 ms, while the bunch density of the coldest ions increases by up to a factor of 10. By studying the time constants of the dependence of ion loss and axial temperature on the magnetic field strength, we exclude the effects of ions loss through the cyclotron motion on the axial ion temperature.