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In this work we investigate the theory for three different uni-directional population transfer schemes in trapped multilevel systems which can be utilized to cool molecular ions. The approach we use exploits the laser-induced coupling between the internal and motional degrees of freedom so that the internal state of a molecule can be mapped onto the motion of that molecule in an external trapping potential. By sympathetically cooling the translational motion back into its ground state the mapping process can be employed as part of a cooling scheme for molecular rotational levels. This step is achieved through a common mode involving a laser-cooled atom trapped alongside the molecule. For the coherent mapping we will focus on adiabatic passage techniques which may be expected to provide robust and efficient population transfers. By applying far-detuned chirped adiabatic rapid passage pulses we are able to achieve an efficiency of better than 98% for realistic parameters and including spontaneous emission. Even though our main focus is on cooling molecular states, the analysis of the different adiabatic methods has general features which can be applied to atomic systems.
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We propose speeding up a single ion heat pump based on a tapered ion trap. If a trapped ion is excited in an oscillatory motion axially the radial degrees of freedom are cyclically expanded and compressed such that heat can be pumped between two reservoirs coupled to the ion at the turning points of oscillation. Through the use of invariant-based inverse engineering we can speed up the process without sacrificing the efficiency of each heat pump cycle. This additional control can be supplied with additional control electrodes or it can be encoded into the geometry of the radial trapping electrodes. We present novel insight how speed up can be achieved through the use of inverted harmonic potentials and verified the stability of such trapping conditions.
Specific heat of dipolar glasses does not obey Debye law. It is of interest to know if the non-Debye specific heat can be accounted for in terms of Schottky-type specific heat arising from rotational tunneling states of the dipoles. This paper deals with rotational tunneling spectra of NH$_{4}^{+}$ ions and the non-Debye specific heat of mixed salts (e.g. (NH$_{4})_{x}$Rb$_{1-x}$Br) of ammonium and alkali halides which are known to exhibit dipolar glass phase. We have measured specific heat of above mixed salts at low temperatures (1.5 K $< T <$ 15 K). It is seen that while the specific heat of pure salts obeys Debye law, the specific heat of mixed salts does not obey Debye law. We have studied the effect of the NH$_{4}^{+}$ ion concentration, first neighbor environment of NH$_{4}^{+}$ ion and the lattice strain field on the non-Debye specific heat by carrying out measurements on suitably chosen mixed salts. Independent of above, we have measured the rotational tunneling spectra, $f(omega $), of the NH$_{4}^{+}$ ions in above salts using technique of neutron incoherent inelastic scattering. The above studies show that both the non-Debye specific heat and the tunneling spectra of the NH$_{4}^{+}$ ions depend on the NH$_{4}^{+}$ ion concentration, first neighbor environment of NH$_{4}^{+}$ ions and the lattice strain field. We have further shown that the temperature dependence of the measured specific heat can be explained for all the samples in terms of a model that takes account of contributions to the specific heat from the Debye phonons and the rotational tunneling states of the NH$_{4}^{+}$ ions. To the best of our knowledge, this is a first study where it is shown that measured specific heat of (NH$_{4})_{x}$Rb$_{1-x}$Br can be quantitatively explained in terms of an experimentally measured rotational tunneling spectra $f(omega $) of the NH$_{4}^{+}$ ions.
The fundamental assumption of statistical mechanics is that the system is equally likely in any of the accessible microstates. Based on this assumption, the Boltzmann distribution is derived and the full theory of statistical thermodynamics can be built. In this paper, we show that the Boltzmann distribution in general can not describe the steady state of open system. Based on the effective Hamiltonian approach, we calculate the specific heat, the free energy and the entropy for an open system in steady states. Examples are illustrated and discussed.
We investigate magic-wavelength trapping of ultracold bialkali molecules in the vicinity of weak optical transitions from the vibrational ground state of the X$^1Sigma^+$ potential to low-lying rovibrational states of the b$^3Pi_0$ potential, focussing our discussion on the $^{87}$Rb$^{133}$Cs molecule in a magnetic field of $B=181,$G. We show that a frequency window exists between two nearest neighbor vibrational poles in the dynamic polarizability where the trapping potential is near magic for multiple rotational states simultaneously. We show that the addition of a modest DC electric field of $E=0.13,text{kV}/text{cm}$ leads to an exact magic-wavelength trap for the lowest three rotational states at a angular-frequency detuning of $Delta_{v=0} = 2pitimes 218.22$,GHz from the X$^1Sigma^+ (v=0, J=0)rightarrow$ b$^3Pi_0 (v=0, J=1)$ transition. We derive a set of analytical criteria that must be fulfilled to ensure the existence of such magic frequency windows and present an analytic expression for the position of the frequency window in terms of a set of experimentally measurable parameters. These results should inform future experiments requiring long coherence times on multiple rotational transitions in ultracold polar molecules.
Sympathetic cooling of molecular ions through the Coulomb interaction with laser-cooled atomic ions is an efficient tool to prepare translationally cold molecules. Even at relatively high collisional energies of about 1$,$eV ($Tsim 10000 ,$K), the nearest approach in the ion-ion collisions never gets closer than $sim$$1,$nm such that naively perturbations of the internal molecular state are not expected. The Coulomb field may, however, induce rotational transitions changing the purity of initially quantum state prepared molecules. Here, we investigate such rotational state changing collisions for both polar and apolar diatomic molecular ions and derive closed-form estimates for rotational excitation based on the initial scattering energy and the molecular parameters.
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