Measuring and manipulating the temperature of cold molecules trapped on a chip

S. Marx, D. Adu Smith, G. Insero, S. A. Meek, B. G. Sartakov, G. Meijer, and G. Santambrogio

Phys. Rev. A 92, 063408 – Published 9 December 2015

Abstract

Following Marx et al. [Phys. Rev. Lett. 111, 243007 (2013)], we discuss the measurement and manipulation of the temperature of cold CO molecules in a microchip environment. In particular, we present a model to explain the observed and calculated velocity distributions. We also show that a translational temperature can be extracted directly from the measurements. Finally, we discuss the conditions needed for an effective adiabatic cooling of the molecular ensemble trapped on the microchip.

Received 3 August 2015
Revised 21 October 2015

DOI:https://doi.org/10.1103/PhysRevA.92.063408

Authors & Affiliations

S. Marx¹, D. Adu Smith¹, G. Insero², S. A. Meek³, B. G. Sartakov⁴, G. Meijer^1,5, and G. Santambrogio^1,2,*

¹Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany
²Istituto Nazionale di Ottica CNR and LENS, Via N. Carrara 1, 50019 Sesto Fiorentino, Italy
³Max-Planck-Institut für Biophysikalische Chemie, Am Fassberg 11, 37077 Göttingen, Germany
⁴A. M. Prokhorov General Physics Institute, RAS, Vavilov Street 38, Moscow 119991, Russia
⁵Institute for Molecules and Materials, Radboud University of Nijmegen, Heijendaalseweg 135, 6525 AJ Nijmegen, Netherlands

^*Present address: INRIM Istituto Nazionale di Ricerca Metrologica, Sesto Fiorentino, Italy; gabriele.santambrogio@fhi-berlin.mpg.de

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Vol. 92, Iss. 6 — December 2015

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Images

Figure 1
(a) Detection region of the chip. Molecules trapped above the microelectrode array (red dots) are released from the traps at a well-defined velocity, whereupon they travel into the detection region of the chip. The molecules are ionized using the REMPI process and are then propelled by the electric field created between the anode and the cathode (a ring electrode) to the ion lenses (not shown), which image the ion spatial distribution on a microchannel plate with phosphor screen. A CCD camera records the resultant image. The microtraps are spaced by 120 $μ m$ , and the diagram is not to scale; the actual distances are marked for reference. (b) Example 2D image of molecules released from an array of microtraps [14]. (c) Integrated line profile of the image in (b).
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Figure 2
(a) Integrated line profiles (black) from images of molecules for differing microelectrode voltages (i.e., differing trap depths), along with the results of numerical trajectory simulations [red (gray)]. The maximal relative speed $v_{max} = \sqrt{2 U / m}$ of stably trapped molecules (given by the trap depth $U$ ) was 2.4, 4.0, 5.1, and 6.1 m/s, respectively. The vertical scale is the same for all data sets. (b) Corresponding speed distributions (red solid line) extracted from the trajectory simulations, along with the best-fit Maxwell-Boltzmann curve (blue dashed line), labeled with the best-fit temperature. Speeds are given relative to the mean forward velocity of the molecular cloud.
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Figure 3
(a) Energy distribution from trajectory simulations, calculated for the same conditions as in Fig. 2 for the 160-V case [solid red (light gray) line]. In blue (dark gray), the energy distributions obtained by integrating the analytical expression of the trapping potential are shown for the cutoff values of 55 and 40 mK. (b) Comparison with the distribution obtained from the traps with more regular shapes: conical, harmonic, and logarithmic traps. All distributions are normalized.
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Figure 4
(a) Integrated line profiles (black) extracted from images (as in Fig. 1) for various expansion times [14]. For each expansion time, the blue (dark gray) line is the result of fitting a multi-Gaussian profile (see text for details); the red (light gray) line is the result of trajectory simulations. (b) The square of the mean Gaussian standard deviation from the fit in (a) plotted against the ballistic expansion time squared. The slope is proportional to the temperature of the gas [Eq. (1)]. (c) Speed distributions calculated from trajectory simulations for all four experimental conditions [red (light gray)] and calculated Maxwell-Boltzmann distributions [blue (dark gray)], with the best fit given by a thick line.
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Figure 5
(a) Experimental integrated line profiles of molecules for various manipulation times, along with corresponding numerical trajectory simulations. The data for the measurement at $t_{a} = 0$ and 188 $μ s$ are the same as in Ref. [14]. By fitting a multi-Gauss function to the experimental and calculated data, values of $σ$ for all four data sets are obtained and are indicated in each panel (the values for the calculated data are shown in parentheses). The relative uncertainty on the determination of $σ$ is 10%. (b) Decrease in temperature with manipulation time from trajectory simulations. Circles denote the times for which experimental measurements were performed. (c) Translational temperature of the clouds for the different expansion times $t_{a}$ as a function of the estimated initial cloud size, obtained from experimental data using Eq. (1). The uncertainty due to the error in the determination of $σ$ is represented by the thickness of the lines. Solid lines show the results for $t_{b} = 15 μ s$ ; dashed lines show the results for $t_{b} = 18 μ s$ . The red circles show $σ_{i}^{2}$ from trajectory simulations.
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