Scanning tunneling microscopy for ultracold atoms

We propose a versatile experimental probe for cold atomic gases analogous to the scanning tunneling microscope (STM) in condensed matter. This probe uses the coherent coupling of a single particle to the system. Depending on the measurement sequence, our probe allows us to obtain either the local density and spatial density correlations, with a resolution on the nanometer scale, or the single particle correlation function in real time. We discuss applications of this scheme to the various possible phases for a two dimensional Hubbard system of fermions in an optical lattice.

Figure 1

(Color online) Sketch of the cold atom tunneling microscope. As an example the application to an antiferromagnetic state with alternating spin states labeled by different colors is shown.

Figure 2

(Color online) Two-photon Raman coupling of the ion $|i⟩$ and an atom $|a_j⟩$ in a harmonic potential well to a molecular ion bound state $|i+a_j⟩$. The single photon coupling is detuned by $\Delta$ from a resonant transition to suppress spontaneous emission from the intermediate excited state. The effective two-photon Rabi frequency ${\Omega }_0$ is proportional to the coefficients of the single photon transitions and inversely proportional to the detuning $\Delta$, i.e., ${\Omega }_0\propto {\Omega }_1{\Omega }_2/\Delta$.

Figure 3

(Color online) Schematics of the experimental sequence for the tunneling mode. The atomic ion $|i⟩$ is introduced at the lattice site $j$ into the many-body system in state $|{\Psi }_0⟩$. The two-photon Raman process (red) couples an atom at this lattice site $|a_j⟩$ to the ion with a certain amplitude. Subsequently, the ion and the many-body system are separated for the probe time $t_0$ during which they evolve individually. After recombination, the Raman interaction is applied again and the molecule formation is detected.

Figure 4

(Color online) The Fourier transform of the temporal correlation function in an $s$-wave and a $d$-wave superconducting state is shown for a gap value of ${\Delta }_0=0.3J$.