Diagrammatic calculation of energy spectrum of quantum impurity in degenerate Bose-Einstein condensate

In this paper we considered a quantum particle moving through delute Bose-Einstein condensate at zero temperature. In our formulation the impurity particle interacts with the gas of uncoupled Bogoliubov's excitations. We constructed the perturbation theory for the Green's function of the impurity particle with respect to the impurity-condensate interaction employing the coherent-state path integral approach. The perturbative expansion for the Green's function is resumed into the expansion for its poles with the help of the diagrammatic technique developed in this work. The dispersion relation for the impurity clothed by condensate excitations is obtained and effective mass is evaluated beyond the Golden rule approximation

THE CO-DIMER: NEW STATES AND TUNNELING SPLITTING

Author Institution: I. Physikalisches Institut, University of Cologne; I. Physikalisches Institut, Institute of SpectroscopyNew extensive millimeter-wave measurements of the $^{12}C^{16}O$ dimer have been made and more than 250 new spectral transitions have been observed in the frequency range of 80 - 135 GHz. Joint analysis of these and previous millimeter-wave data yielded in determination and precise location of 34 new energy levels of $A^{+}$ -symmetry and 21 levels of $A^{-}$-symmetry. Some of them belong to already known stacks and others make up 9 new stacks of the dimer. These new energy levels are located at energies from 8 to $18 cm^{-1}$ and in a free rotation limit they correspond to the states with $(j_{1}, j_{2}, K) = (1, 1, 0), (1, 1, 1), (1, 1, 2)$ and (2, 0, 2), where j is a rotational quantum numbers of the CO monomer and K is a projection of the total angular momentum on the intermolecular axis. One newly observed state of $A^{+}$ -symmetry originating at $12 cm^{-1}$ has $K = 0$ and might be tentatively attributed to the lower tunneling component of the stretching vibration of the CO-dimer. The tunneling splitting for many different states of two isotopic modifications of the dimer, $(^{12}C^{16}O)_{2}$ and $(^{13}C^{16}O)_{2}$ was determined, and its dependence on J-, K- values and on isotopic mass was studied. For some states the tunneling splitting increases in $(^{13}C^{16}O)_{2}$ as compared to $(^{12}C^{16}O)_{2})$. Possible explanations of this anomalous behavior will be discussed

MILLIMETER-WAVE SPECTRA OF CARBON MONOXIDE SOLVATED WITH HELIUM ATOMS

J.~Tang, A.~R.~W.~McKellar, J.~Chem.~Phys. 119, 763 (2003); A.~R.~W.~McKellar, J.~Chem.~Phys. 121, 6868 (2004); A.~R.~W.~McKellar, J.~Chem.~Phys. 125, 164328 (2006).L.~A.~Surin, A.~V.~Potapov, B.~S.~Dumesh, S.~Schlemmer, Y.~Xu, P.~L.~Raston, and W.~Jager, Phys.~Rev.~Lett. 101, 233401 (2008).T.~Skrbic, S.~Moroni, and S.~Baroni, J.~Phys.~Chem.~A 111, 7640 (2007).K.~von Haeften, S.~Rudolph, I.~Simanovski, M.~Havenith, R.~E.~Zillich, and K.~B.~Whaley, Phys.~Rev.~B 73, 054502 (2006).Author Institution: I. Physikalisches Institut, University of Cologne, 50937 Cologne, Germany; Institute of Spectroscopy of Russian Academy of Sciences, 142190 Troitsk, Moscow region, RussiaMillimeter-wave spectra of He$_N-$CO ($^{12}$C$^{16}$O, $^{13}$C$^{16}$O, $^{12}$C$^{18}$O, $^{13}$C$^{18}$O) clusters with $N$ up to 10, produced in a molecular expansion, were observed using intracavity OROTRON jet spectrometer in the frequency range of 110-150 GHz. The $R$(0) transitions were detected, which correspond to the known $b$-type ($K$ = 1 $-$ 0) $R$(0) lines of the binary system, He$_1-$CO. Further, the $a$-type ($K$ = 0 $-$ 0) rotational transitions of He$_N-$CO ($N$ = 7, 8) in the frequency range of 20-40 GHz were measured combining OROTRON spectrometer with a double resonance technique. The isotopic shifts of the cluster transitions show remarkably smooth behavior with $N$ from 1 to 6 and become rather scattering for $N$ $\geq$ 7. The dependence of the rotational constant (cluster moment of inertia) and of the shift of the CO fundamental vibration on the number of He atoms in cluster were obtained for He$_N-$CO isotopologues from the analysis of their infrared spectra and very recent microwave data for the normal He$_N-^{12}$C$^{16}$O isotopologue . This study explores the microscopic evolution of superfluidity, which becomes apparent even in such small clusters as He$_4-$CO. The obtained results are compared with those from recent quantum Monte-Carlo calculations and used to further interpret recent infrared measurements of CO in helium nanodroplets

NEW MILLIMETER-WAVE INTRACAVITY JET SPECTROMETER BASED ON OROTRON

Author Institution: Institute of Spectroscopy, Russian Academy of Sciences; I. Physical Institute, University of CologneA new highly sensitive millimeter-wave spectrometer has been developed for the investigation of weakly bounded van der Waals molecular complexes produced in a supersonic jet expansion. The main feature of the spectrometer is that the molecular jet expands into the high quality $(Q = 10^{4})$ resonator of a tunable coherent source of radiation - OROTRON (106- 150 GHz). The absorption of the radiation inside the cavity is detected by the variation of the electron current of the orotron in a collector circuit. This simple method of detection and the narrow linewidth of the orotron radiation (10-15 kHz) without any frequency and phase stabilization make this spectrometer very simple and convenient for searching of new lines and for recording of weak spectra. The large effective length of absorption results in an improvement of sensitivity for more than two orders of magnitude in comparison with the existing single path schemes. The new set-up has been adjusted and tested by the observation of the isotopomers of CO in natural abundance. The rotational transition $J = 1 - 0$ of isotopic species $^{13}C^{17}O (0.000\%)$ with partially resolved quadrupole structure was observed. The measurements of the $K = 1 - 0$ high-J $(10<J<20)$ pure rotational transitions of Ar-CO and the first observation of Ne-CO (for${^{20.21,22}}Ne$ isotopes in natural abundance) in millimeter-wave range have been made. The analysis of these data will be presented

The Problem of the Structure (State of Helium) in Small He-N-CO Clusters

A second-order perturbation theory, developed for calculating the energy levels of the He-CO binary complex, is applied to small He-N-CO clusters with N = 2-4, the helium atoms being considered as a single bound object. The interaction potential between the CO molecule and He-N is represented as a linear expansion in Legendre polynomials, in which the free rotation limit is chosen as the zero approximation and the angular dependence of the interaction is considered as a small perturbation. By fitting calculated rotational transitions to experimental values it was possible to determine the optimal parameters of the potential and to achieve good agreement (to within less than 1%) between calculated and experimental energy levels. As a result, the shape of the angular anisotropy of the interaction potential is obtained for various clusters. It turns out that the minimum of the potential energy is smoothly shifted from an angle between the axes of the CO molecule and the cluster of theta = 100 in He-CO to theta = 180 (the oxygen end) in He-3-CO and He-4-CO clusters. Under the assumption that the distribution of helium atoms with respect to the cluster axis is cylindrically symmetric, the structure of the cluster can be represented as a pyramid with the CO molecule at the vertex

Rotational study of carbon monoxide isotopologues in small (4)He clusters

High resolution microwave (a-type) and millimetre-wave (b-type) spectra of HeN–13C16O, HeN–12C18O, and HeN–13C18O clusters (N ≤ 10) were observed, significantly extending the initial spectroscopic observations on HeN–12C16O by Surin et al. [Phys. Rev. Lett., 2008, 101, 233401]. The frequencies of the a-type series, which evolves from the end-over-end rotation of the dimer, decrease from N = 1 to 3, then increase smoothly to at least N = 9. This turnaround indicates a rapid evolution of the solvation character from classical to quantum. The b-type series, which evolves from the free molecule rotation of CO, increases from N = 0 to 6 and then decreases to at least N = 10. This is consistent with an initially increasing anisotropy of the helium environment, followed by a tendency of the solvation shell to become more isotropic. The shift of the vibrational frequency of CO as determined from the infrared [A. R. W. McKellar, J. Chem. Phys., 2004, 121, 6868; ibid., 2006, 125, 164328] and microwave data reveals an approximately linear decrease from N = 1 to at least 9. If the linear shift were to continue until completion of the first solvation shell (N ≈ 14), the estimated helium nanodroplet shift will be well undershot [K. von Haeften, S. Rudolph, I. Simanovski, M. Havenith, R. E. Zillich and K. B. Whaley, Phys. Rev. B: Condens. Matter Mater. Phys., 2006, 73, 054502]. In this case, there must be an upturn in the vibrational shift beyond N = 14, which is not predicted by theory [T. Škrbić, S. Moroni and S. Baroni, J. Phys. Chem. A, 2007, 111, 7640]. By extrapolating the a-type series to N = 14 (assuming a linear vibrational shift), we estimate the rotational constant, B, of CO in the helium nanodroplet to be [similar]74% of its gas phase value. This is in reasonable agreement with simulations (76% at N = 14), which predict the limiting value to be approximately reached upon completion of the first solvation shell (73% at N = 100) [T. Škrbić, S. Moroni and S. Baroni, J. Phys. Chem. A, 2007, 111, 7640]. However, this value is significantly larger than that inferred from helium nanodroplet experiments (63%).P. L. Raston, Y. Xu, W. Jäger, A. V. Potapov, L. A. Surin, B. S. Dumesh and S. Schlemme

Rotational study of carbon monoxide solvated with helium atoms

High resolution microwave and millimeter-wave spectra of HeN-CO clusters with N up to 10, produced in a molecular expansion, were observed. Two series of J = 1-0 transitions were detected, which correspond to the a-type and b-type J = 1-0 transitions of He1-CO. The B rotational constant initially decreases with N and reaches a minimum at N = 3. Its subsequent rise indicates the transition from a molecular complex to a quantum solvated system already for N = 4. For N > or =6, the B value becomes larger than that of He1-CO, indicating an almost free rotation of CO within the helium environment.L. A. Surin, A. V. Potapov, B. S. Dumesh, S. Schlemmer, Y. Xu, P. L. Raston, and W. Jäge