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Experimental Setup and Probing

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Non-Equilibrium Dynamics Beyond Dephasing

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Abstract

This chapter serves as an introduction to the experimental setup. It discusses the tools and techniques developed to create and probe the 1d Bose gases described in Chap. 2. First, Sect. 3.1 reviews basic experimental techniques until Sect. 3.2 describes the experimental setup and cycle. Both of these discussion are kept brief as there exists a vast body of literature and theses on these topics.

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Notes

  1. 1.

    As for Eq. (3.1), this expression is valid as long as the fields are small enough such that the magnitude of \(\mathbf {F}\) remains a good quantum number.

  2. 2.

    Assuming that all detunings are much larger than the excited state hyperfine splitting.

  3. 3.

    The ground state hyperfine splitting in \(^{87}\)Rb is 6.8 GHz [5] while the for typical parameters in our setup the Zeeman state splitting in the center of the undressed trap is \({\sim }{390}\,{\mathrm{kHz}}\) (see Sect. 3.2.2).

  4. 4.

    \(10^{-10}\) mbar, pumped by an ion pump (Varian 150 l/s Star-Cell) and a titanium sublimation pump.

  5. 5.

    Tabor Electronics WW1071.

  6. 6.

    A 6.81 GHz oscillator mixed with a sweepable \({0}-{30}\,{\mathrm{MHz}}\) source (SRS DS345) or/and a sweepable \({1}-{150}\,{\mathrm{MHz}}\) source (VFG150).

  7. 7.

    Coherent MBR-110 pumped by a Coherent Verdi V18.

  8. 8.

    Toptica LD-0780-0080-DFB-1 in a ThorLabs LDM21 mount.

  9. 9.

    In Fig. 3.5, the first and second U-wire pairs correspond to the left and right U-wires. A difference in the currents flowing in these pairs allows to move the trap along the main trapping wire. For us, the optimal position is chosen by finding a region where the potential is sufficiently flat, least perturbed by wire corrugations.

  10. 10.

    \(\lambda = {767}\,{\mathrm{nm}}\), Toptica DLX 110.

  11. 11.

    The optical setup was previously used with resonant light. It was designed to selectively pump parts of the cloud into a dark state for tomographic imaging. More information can be found in [31] and the supplementary materials of [42].

  12. 12.

    The expressions for \(E_\mathrm {kin}\) and \(E_\mathrm {int}\) in the broadened case are obtained by integrating over the transverse degrees of freedom for the kinetic and the interaction term of the Hamiltonian given in Eq. (2.30). Equation (3.7) was also found in [47].

  13. 13.

    In Ref. [48] a similar density dependence of the width in expansion was measured experimentally, though the interpretation of the results has some shortcomings. No argument was given as to why it makes sense to compare the scaling of the measured density distribution width in expansion to the scaling of the in situ wave function width. Further, the expression for the width used was taken from [49], which reproduces the broadened chemical potential well but deviate significantly from the width found in [50] and the width obtained from numerical simulations of the radial GPE.

  14. 14.

    For the harmonic longitudinal confinement typically \(\omega _{\perp }\,/\, \omega _z \;\sim \; 200\).

  15. 15.

    For the box trap it would be \(t_\mathrm {tof}\ll L/c\pi \).

  16. 16.

    Note that the influence of the in situ density fluctuations on the final ripple pattern mainly stems from their modulation of the initial pre-expansion density profile.

  17. 17.

    Calculating the number of fringes within the full \(1/e^2\)-width we obtain \(\frac{2\sqrt{2}\sigma _{t,n}}{\lambda _\mathrm {fs}} = \frac{\sqrt{2}}{\pi }\frac{d}{a_{\perp }}\root 4 \of {1 + 2a_s n_\mathrm {1d}}\).

  18. 18.

    Andor DV435-BV-958.

  19. 19.

    The strategy here is to maximize the \(g_2\) contrast \(C_{g_2}\) or to find the smallest minimum position \(\delta z_\mathrm {min}\) for a given expansion time. See Sect. 3.3.3 for a definition of these quantities.

  20. 20.

    This was concluded only from simulations as a sensitive measurement of the effective spot size, as through the density ripples correlations in the case of long expansion times, is not possible.

  21. 21.

    Possible non-linearities due to different saturation levels are neglected.

  22. 22.

    Semrock SEM-LL01-780-25.

  23. 23.

    Even though the filters are mounted parallel to each other, most of the dipole light probably hits the filters at a small angle. For a large separation this causes the light to undergo only a small number of reflections before exiting the inter-filter cavity and being dumped, leading to a higher total optical density.

  24. 24.

    Andor iXon DV887DCS-BV. An EMCCD camera used without the electron multiplier mode.

  25. 25.

    Uniblitz LS6. This shutter takes 0.7 ms to fully open its 6 mm wide aperture.

  26. 26.

    Andor DV435-BV-958.

  27. 27.

    The peak height was the observable used for thermometry in [59].

  28. 28.

    Numerically we observe that this relation breaks down when the size of the density modulations emerging in expansion get comparable to the average density.

  29. 29.

    The soundness of this phenomenological consideration of the imaging resolution was confirmed by numerical simulations if the imaging process. Numerical integration was performed using the novel technique found in Ref. [71].

  30. 30.

    The parameter \(\Delta _\mathrm {rf}\) gives the relative difference of the squared peak-to-peak amplitude of the applied voltages, translating into a current amplitude imbalance. Due to possible differences in resistance \(\Delta _\mathrm {rf} = 0\) does not equate balanced rf currents.

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  1. Laboratoire Kastler Brossel, École Normale Supérieure, Paris, France

    Bernhard Rauer

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Rauer, B. (2019). Experimental Setup and Probing. In: Non-Equilibrium Dynamics Beyond Dephasing. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-18236-6_3

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