Measurement-Induced Localization of an Ultracold Lattice Gas

The process of measurement can modify the state of a quantum system and its subsequent evolution. Here, we demonstrate the control of quantum tunneling in an ultracold lattice gas by the measurement backaction imposed by the act of imaging the atoms, i.e., light scattering. By varying the rate of light scattering from the atomic ensemble, we show the crossover from the weak measurement regime, where position measurements have little influence on tunneling dynamics, to the strong measurement regime, where measurement-induced localization causes a large suppression of tunneling—a manifestation of the quantum Zeno effect. Our study realizes an experimental demonstration of the paradigmatic Heisenberg microscope and sheds light on the implications of measurement on the coherent evolution of a quantum system.

Figure 1

(a) Lattice imaging scheme: An atom within a lattice site is cooled to the ground state $|D⟩\equiv |F=1,m_F=+1;\nu =0⟩$ via RSC. This state is nominally a “dark state”; i.e., it does not emit fluorescence. An auxiliary “imaging” beam promotes the atom out of this state to a fluorescing state $|B⟩$ which is subsequently cooled back to $|D⟩$. Repeated cycles of this process extract fluorescence from the atom while continually restoring the atom to $|D⟩$. (b) The imaging scheme thus allows us to distinguish between two possible states of the atom—a bright state $|B⟩$ that can be imaged and a dark state $|D⟩$ that cannot be imaged. (c) Fluorescence images of a lattice gas obtained at increasing levels of the measurement rate ${\mathrm{\Gamma }}_m$. The field of view of each frame is $250\mu \mathrm{m}\times 250\mu \mathrm{m}$.

Figure 2

Photoassociation measurements demonstrating the crossover from the weak measurement regime (${\mathrm{\Gamma }}_m\ll J$) to the strong measurement regime (${\mathrm{\Gamma }}_m\gg J$). In the former regime (a), position measurements have little influence on tunneling, and the two-body lifetime $\tau ={\kappa }^{-1}$ is independent of the imaging rate. In the latter regime (b), measurement-induced localization suppresses tunneling rates leading to an increase of the two-body lifetime. (c) Measurements of two-body lifetime vs measurement rate. These data were obtained at a lattice parameter $s=8.5(2.0)$ with ${\tau }_0=31(3)\mathrm{ms}$.

Figure 3

In the strong measurement regime, the effective tunneling rate is given by ${\tilde{J}}_{\mathrm{eff}}\sim J^2/{\mathrm{\Gamma }}_m$. This leads to a two-body lifetime $\tau ={\kappa }^{-1}$ that linearly increases [as seen in (a)] with the measurement rate—a clear signature of the QZE. These data were obtained for $s=23(2)$. (b) The quadratic scaling of the effective tunneling rate (and, hence, the photoassociation rate $\kappa$) with the bare lattice tunneling rate is demonstrated by measurements of $\kappa$ for lattice gases confined in different lattice depths. These data were obtained by imaging the lattice gases at fixed measurement rate ${\mathrm{\Gamma }}_m$. The dashed line shows a quadratic fit to the data.

Figure 4

Suppression of atomic diffusion due to position measurements. A brief on-resonant optical pulse depletes the central region of the lattice gas [indicated by the arrow in (a)]. (b) Cross section of the atomic ensemble following this pulse. (c) Atoms rapidly diffuse into this central region in the absence of imaging (blue, $s=8.5$, ${\mathrm{\Gamma }}_m=0$). In contrast, diffusion is suppressed when the atoms are continuously imaged (red, $s=8.5$, ${\mathrm{\Gamma }}_m=1000{\mathrm{s}}^{-1}$).

Figure 5

For measurement rates ${\mathrm{\Gamma }}_m$ that exceed the Raman cooling rate ${\mathrm{\Gamma }}_{\mathrm{RSC}}$, atoms are promoted to higher vibrational bands because of the measurement. The increased tunneling rates in these higher bands cause a deviation from the linear scaling of the lifetime $\tau$ with ${\mathrm{\Gamma }}_m$. Because of the proportionate relation between the Raman cooling rate and the lattice depth, this deviation occurs more readily for atoms in shallow lattices. The data shown represent two-body lifetimes in the Zeno regime for lattice parameters $s=9.5(1.5)$, (filled square), $s=21(2)$, (filled circle). The shaded region represents a Monte Carlo simulation of a kinetic model of the measurement process. Inset: Simulated two-body lifetimes vs measurement rate: The onset of higher-band tunneling occurs at larger ${\mathrm{\Gamma }}_m$ for increasing Raman cooling rates (bottom to top).