Suppression and enhancement of bosonic stimulation by atomic interactions

Abstract

The tendency of identical bosons to bunch, seen in the Hanbury Brown-Twiss effect and Bose-Einstein condensation, is a hallmark of quantum statistics. This bunching can enhance the rates of fundamental processes such as atom-atom and atom-light scattering when atoms scatter into already occupied states. For non-interacting bosons, the enhancement of light scattering follows directly from the occupation of the atom's final momentum state. Here, we study scattering between off-resonant light and atoms in a quasi-homogeneous Bose gas with tunable interactions and show that even weak interactions, which do not significantly alter the momentum distribution, strongly affect atom-light scattering. Changes in local atomic correlations suppress the bosonic enhancement under weak repulsive interactions and increase the scattering rate under attractive ones. Moreover, if the interactions are rapidly tuned, light scattering reveals correlation dynamics that are orders of magnitude faster than the collisional dynamics of the momentum-space populations. Its extreme sensitivity to correlation effects makes off-resonant light scattering a powerful probe of many-body physics in ultracold atomic gases.

Figures (11)

• Figure 1: Bosonic enhancement of atom-light scattering in an interacting gas.a, Experimental concept. We illuminate a quasi-homogeneous Bose gas (blue) held in an optical box trap (red) with an off-resonant laser beam and detect photons scattered at an angle of 35$^{\rm o}$. Scattering of photons from wavevector ${\bf q}$ to ${\bf q} - {\bf Q}$ corresponds to atom recoil $\hbar {\bf Q}$. b, Cartoon of the effects of quantum degeneracy and atomic interactions on atom-light scattering. Here $d$ is the inter-particle spacing (set by the gas density), $\lambda$ is the thermal de Broglie wavelength (the size of the blue atomic wave-packets), and the $s$-wave scattering length $a$ gives the strength of interactions. The scattered-light intensity is indicated by the thickness of the red arrows. In a degenerate non-interacting gas, with $\lambda \gtrsim d$ and $a=0$, scattering is enhanced by interference of light scattered by overlapping wave-packets. However, this overlap and enhancement are reduced by repulsive interactions ($a>0$). c, Illustration of the local effect of interactions; here $T \approx 1.1\, T_{\textrm{c}}$, where $T_{\textrm{c}}\approx 200\,$nK is the critical temperature for Bose--Einstein condensation. Reducing $a$ from $500\,a_0$ to $<50\,a_0$ within $200\,\upmu$s (top panel) enhances atom-light scattering on the same timescale (bottom panel), which is too short to change the global momentum-space occupations or the gas density distribution (see text). For each measurement, at different times during the interaction ramp, the light pulse was applied for $10\,\upmu$s, and the single-particle scattering rate $\Gamma_0$ corresponds to $27$ photon counts. Each data point represents the average of $107$ independent experimental runs, and the error bars indicate the standard error of the mean (s.e.m.).
• Figure 1: Linearity of the response. We show the linearity of the recorded photon count with the time-integrated intensity of the atom-light scattering pulse. We always work with light pulses such that the scattered-photon count is $\lesssim 60$. We estimate that this corresponds to $\lesssim 0.1$ photons scattered per atom.
• Figure 2: Effects of quantum degeneracy and interactions.Here, the error bars denote the s.e.m.a, The bosonic enhancement factor, $E=\Gamma/\Gamma_0$, as a function of the reduced temperature $T/T_{\textrm{c}}$ for a quasi-ideal gas ($a = 25\,a_0$). The increase of enhancement with the gas density $n$ or when approaching condensation is captured well by mean-field numerical calculations (solid lines). Data points show averages over independent experimental runs, with $132$, $150$ and $100$ repetitions for the lowest to highest density, respectively.b,$E$ versus $T/T_{\textrm{c}}$ for different interaction strengths and fixed $n = 10µ m^{-3}$. Mean-field effects (the differences between the three solid lines) do not explain the dramatic suppression of bosonic enhancement. All data corresponds to the mean of 150 independent experiments.
• Figure 2: Box sharpness. Main panel: temperature dependence of the condensed fraction, obtained using Eq. (\ref{['eq:si:1']}) with $\gamma_{\rm fit} =10$, is fitted well to Eq. (\ref{['eq:si:2']}) with the consistent $\gamma_{\eta} =10$ (dashed line). Each data point is the average of 93 independent measurements and the error bars denote the standard deviation. Inset: $\gamma_{\eta}$ obtained for different $\gamma_{\rm fit}$; the consistency requirement $\gamma_{\eta} = \gamma_{\rm fit}$ (dashed line) gives $\gamma = \gamma_{\eta} = \gamma_{\rm fit} = 10$.
• Figure 3: Beyond-mean-field interaction effects. Here we fix $n = 10 \, \upmu{\rm m}^{-3}$ and $T = T_{\textrm{c}}$, and perform spin-flips from the $\ket{1,-1}$ to the $\ket{1,0}$ atomic state at different magnetic fields to realize sub-$\upmu$s interaction quenches and study the subsequent evolution of $E$ on microsecond timescales, when only local correlations can change. For all data, the error bars represent the s.e.m. and$E$ is measured using $4\,\upmu$s-long light-scattering pulses. a, $a(B)$ for the two spin states, with the dashed lines indicating Feshbach resonances (where $|a| \rightarrow \infty$). The symbols and arrows depict the spin-flips in b, and the shaded regions show the $B$-field ranges, near two different $\ket{1,0}$ resonances, used in c. b, Correlation dynamics. Independently of the initial and final value of $a$, the light-scattering rate adjusts to the quench at $t=0$ within the same time of $\approx 50\,\upmu$s; exponential fits (solid lines) give a time-constant $\tau=25(5)µs$. Here, each data point represents the average of $116$ repetitions.c, Quasi-steady-state $E$, measured $50\,\upmu$s after the quench from $a<40\,a_0$ in $\ket{1,-1}$ to $a = (35-750)\,a_0$ in $\ket{1,0}$; the symbol colors match the shadings in a. Plotting $E$ versus $a/\lambda$ shows that a scattering length an order of magnitude smaller than the size of the wave packets and the inter-particle distance (see Fig. \ref{['fig1']} b) is sufficient to almost completely suppress bosonic enhancement. The solid line shows the steady-state $E$ predicted by our beyond-mean-field calculations (see text) and the dashed line includes the correction for the fact that in $2\tau$ the correlations do not yet fully settle. All data is the mean of $123$ independent experimental runs.