Coherent manipulation of Bose-Einstein condensates with state-dependent microwave potentials on an atom chip

A novel tool for the quantum lab on a chip.

Entanglement-based technologies, such as quantum information processing, quantum simulations, and quantum-enhanced metrology, have the potential to revolutionize our way of computing and measuring and help clarifying the puzzling concept of entanglement itself. Ultracold atoms on atom chips are an attractive system for their implementation, as they provide control over quantum systems in a compact, robust, and scalable setup. An enabling technology in this system is a potential depending on the internal atomic state. Coherent dynamics in such a potential combined with collisional interactions allows entanglement generation both for individual atoms and ensembles.

In the experiment described here (see [1]), we demonstrate coherent manipulation of Bose-condensed atoms in a state-dependent potential, generated in a novel way with microwave near-fields on our atom chip. We reversibly entangle atomic internal and motional states, realizing a trapped-atom interferometer with internal-state labeling. Our system provides control over collisions in mesoscopic condensates, paving the way for on-chip generation of many-particle entanglement and quantum-enhanced metrology with spin-squeezed states.

A ⁸⁷Rb BEC is prepared in a static magnetic trap in a superposition of the hyperfine states |0>=|F=1, mF=-1> and |1>=|F=2, mF=1>, whose favorable coherence properties we have studied in earlier experiments. Internal-state dependence is added to the trapping potential with the help of microwave near-fields. The microwave is coupled into chip wires which form a coplanar microwave guide (CPW, see figure 1).

Figure 1: Atom chip with microwave coplanar waveguides (CPWs).
(a) Photograph of the chip. (b) Schematic close-up of the experiment region. The three central wires (red) form a CPW. All wires (including the CPW) can also carry DC currents for the generation of static magnetic traps. A typical trap position is indicated by the black cross. Equipotential lines for one possible configuration of the microwave near-field potential (see figure 2) are shown.

The microwaves with a frequency of ~6.8 GHz couple hyperfine levels of the F=1 manifold to hyperfine levels of F=2. This coupling leads to state-dependent energy shifts. Due to the strong polarization and amplitude gradients of the microwave near-fields, complex state-dependent potential landscapes can be created. In the present experiments, we selectively create a potential for state |0> by coupling it to an auxiliary state as shown in figure 2.

Figure 2: Ground state hyperfine levels of ⁸⁷Rb. The microwave shown in blue is used to generate a potential selectively for state |0> by coupling it to auxiliary state |2>. All transitions connecting to |1> are far off resonance. The microwave+rf shown in green is for internal-state manipulation on the |0>↔|1> transition.

Figure 3: Absorption images of the adiabatically split BEC. By imaging both hyperfine states simul- taneously (top), only F = 1 (middle), or only F = 2 (bottom), the state-selectivity of the splitting is established.

Figure 4: Movie of the splitting and recombination of the BEC. In this case, both states are imaged.

With the microwave potential gradient, the condensate can be state-selectively split and recombined by shifting the potential minimum of one state with respect to the other. The splitting distance can be larger than 10 µm or several Thomas-Fermi radii which means a complete separation of the two states (see figures 3+4).

To prove the coherence of the manipulation, we have embedded the splitting and recombination sequence in between two π/2 pulses of a Ramsey sequence thus creating a trapped-atom interferometer with internal-state labeling. We apply a first π/2-pulse, creating a superpostion of |0> and |1>. We then turn on the on-chip-microwave, so that state |0> experiences a displaced harmonic potential in which it starts to oscillate. We now apply the second π/2-pulse after a variable duration and record Ramsey interference fringes. Initially, the fringe contrast quickly decays because the wavefunction of state |0> starts to move with respect to state |1> so that the two states do not overlap anymore. However, if we wait for a full oscillation period, the two states overlap again and high contrast Ramsey fringes reappear (see figure 5). This proves that the manipulation is coherent.

An oscillation of state |0> with respect to |1> results in periodic entanglement and disentanglement of internal and motional states of the atoms. This mechanism is at the heart of the quantum phase gate proposed in [2,3]. The gate can be viewed as two state-selective interferometers next to each other, each containing a single atom, where the oscillating states collide and pick up a phase shift, resulting in entanglement between the two atoms.

By controlling the wavefunction overlap between |0> and |1> with the state-dependent potential, our system can be used to tune interactions in a state-dependent way for atoms such as ⁸⁷Rb that do not have convenient Feshbach resonances. We have exploited this for the generation of many-particle entangled states such as spin-squeezed states, as described in [4]. Figure 5: Periodic recurrences of Ramsey interference contrast in the BEC interferometer. The contrast of the Ramsey fringes on the |0>↔|1> transition is modulated due to the periodic splitting and recombination of the motional wave functions.
(a) A running standard deviation of the number of atoms in state |1> as a measure of the wave function overlap. (b) Corresponding Ramsey fringe data for selected values of the Ramsey time T_R. (c) In-situ images of the atomic density distribution for T_R corresponding to the centre of the windows in (b).

For more details about these experiments, see our paper [1].

References

(see also our list of publications)

[1] Böhi, P., Riedel, M. F., Hoffroge, J., Reichel, J., Hänsch, T. W. and Treutlein, P. Coherent manipulation of Bose-Einstein condensates with state-dependent microwave potentials on an atom chip. Nature Physics 5, 592 (2009).
[2] Calarco, T., Hinds, E. A., Jaksch, D., Schmiedmayer, J., Cirac, J. I. and Zoller, P. Quantum gates with neutral atoms: Controlling collisional interactions in time-dependent traps. Phys. Rev. A 61, 022304 (2000).
[3] Treutlein, P., Hänsch, T. W., Reichel, J., Negretti, A., Cirone, M. A. and Calarco, T. Microwave potentials and optimal control for robust quantum gates on an atom chip. Phys. Rev. A 74, 022312 (2006).
[4] Riedel, M. F., Böhi, P., Yun, L., Hänsch, T.W., Sinatra, A. and Treutlein, P. Atom-chip-based generation of entanglement for quantum metrology. Nature, Advance Online Publication, DOI: 10.1038/nature08988