Cavity-aided magnetic resonance microscopy of atomic transport in optical lattices

Journal name:
Nature Physics
Volume:
7,
Pages:
604–607
Year published:
DOI:
doi:10.1038/nphys1967
Received
Accepted
Published online

Ultracold atoms are emerging as an important platform for precision sensing and measurement, quantum information science, and simulations of condensed-matter phenomena. Microscopic imaging is a powerful tool for measuring cold-atom systems, enabling the readout of ultracold atomic simulators1, 2 and registers3, the characterization of inhomogeneous environments4, and the determination of spatially varying thermodynamic quantities5, 6, 7, 8. Cold-atom microscopy has recently been demonstrated with imaging resolution sufficient to detect and address single9 or multiple10 atoms at individual optical-lattice sites with lattice spacings of micrometres11, 12 and below1, 2, 13, 14. However, those methods, which rely either on the fluorescence1, 2, 9, 11, 12, 13 or ionization10, 14 of atoms, destroy the quantum states being measured and have limited dynamic range. Here we demonstrate magnetic resonance imaging of atomic gases in optical lattices, obtained by dispersively coupling atoms to a high-finesse optical cavity. We achieve state-sensitive, single-lattice-site images with high dynamic range. We also apply this technique to measure the non-equilibrium transport dynamics of the gas.

At a glance

Figures

  1. An ensemble of 87Rb atoms is optically trapped within a vertically oriented high-finesse Fabry-Perot cavity.
    Figure 1: An ensemble of 87Rb atoms is optically trapped within a vertically oriented high-finesse Fabry–Perot cavity.

    Copper wires (orange, with current direction indicated) embedded within a 100-μm-thick silicon substrate (grey), together with an external bias coil, produce both a strong vertical magnetic field gradient (|B| contours shown) and a vertical bias field near the atoms. Inset: Atoms (red) are trapped at the antinodes of a standing-wave optical lattice (yellow) with 425nm lattice spacing. Circularly polarized cavity probe light (pink), detuned several gigahertz from the D2 line, acquires a dispersive phase shift that is sensitive to the atom spin projection along the cavity axis.

  2. Single-shot MRI of atoms in an optical lattice.
    Figure 2: Single-shot MRI of atoms in an optical lattice.

    For this image, Δca/2π=−14GHz with 1×107photonss−1 exiting the cavity, and 1,800 atoms initially in the |F,mFright fence=|2,2right fence state. a, The shift ΔNωcω0 of the cavity from its empty resonance frequency (red line, left axis), showing steps as the RF (blue line, right axis) is chirped from high to low. As the RF is swept back, the detuning recovers its initial value with 85% each-way fidelity. b, Atomic density as calculated from the time derivative of ΔN, both uncorrected (red solid line) and corrected (yellow dotted line) for spatially varying sensitivity (probe and trap antinodes are overlapped at site 7). The peak widths (200nm FWHM) are given by the convolution of the imaging resolution (150nm), the atom-distribution width (100nm), and a low-pass analysis filter (90nm). The image has an offset of 80atomμm−1 due to deterministic atom loss (dotted line). c, The imaging resolution is proportional to the ratio of the 14kHz magnetic resonance width to the 114kHzμm−1 gradient of the magnetic resonance frequency. The magnetic resonance width is measured by sweeping over resonance in a uniform bias field (red solid line) and fitting to adiabatic-passage theory (blue dashed line).

  3. Single-shot measurement of number of atoms in a single lattice site.
    Figure 3: Single-shot measurement of number of atoms in a single lattice site.

    The RF sweep (blue, left axis, solid line at full amplitude, dashed line at zero amplitude) is halted for a measurement period (shaded area), then swept across the lattice site of interest, before halting and measuring again. The number of atoms is calculated from the cavity shift (orange, right axis) after correcting for deterministic atom loss (red, right axis, corrected about t=9.5ms). Here Δca/2π=−14GHz, corresponding to 122atomsMHz−1 of cavity shift. The inset shows the Allan deviation of the cavity shift after correcting for atom loss, using the probe frequency only (blue circles) and corrected using the instantaneous cavity transmission (green squares). The dotted line is the expected deviation due to photon shot noise. The deviation on the probe frequency measurement at short times is below the shot-noise expectation due to a 20kHz electronic filter. The 60kHz Allan deviation for τ=2.2ms corresponds to a sensitivity of tenatoms.

  4. Atom transport in an optical lattice as measured using cavity-aided MRI.
    Figure 4: Atom transport in an optical lattice as measured using cavity-aided MRI.

    87Rb atoms at 380nK tunnel resonantly in a 10.1Er lattice with tunnelling matrix element J=planck×380s−1. Left: after allowing the atoms to evolve for a fixed time (t=0.2,1.1,3.0planck/J shown), we use MRI to image the gas, correcting for spatially varying sensitivity. For each evolution time, 15 images are averaged together (red line, right axis), and these are integrated to obtain the atom-number distribution among lattice sites (yellow bars, left axis, orange region indicates 68% certainty as obtained from Allan deviation). Each distribution is then fitted to a Gaussian envelope. Right: position variance σ2 of the Gaussian envelope fit, expressed in units of square lattice spacing, as a function of transport time, expressed in units of inverse tunnelling rate. At early times (t<2planck/J), the data (green circles, error bars denote 68% certainty from fits) agree with no-free-parameter ballistic tunnelling theory (blue line).

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Affiliations

  1. Department of Physics, University of California, Berkeley, California 94720, USA

    • Nathan Brahms,
    • Thomas P. Purdy,
    • Daniel W. C. Brooks,
    • Thierry Botter &
    • Dan M. Stamper-Kurn
  2. Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

    • Dan M. Stamper-Kurn
  3. Present address: JILA, University of Colorado, Boulder, Colorado 80309, USA

    • Thomas P. Purdy

Contributions

Experimental data were taken by T.P.P., N.B., D.W.C.B. and T.B. All authors were involved with experimental design, data analysis, and production of the manuscript.

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The authors declare no competing financial interests.

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