Raman amplification of matter waves

We demonstrate a Raman amplifier for matter waves, where the amplified atoms and the gain medium are in two different hyperfine states. This amplifier is based on a form of superradiance that arises from self-stimulated Raman scattering in a Bose-Einstein condensate.

Figure 1

Observation of superradiant Rayleigh scattering. (a) Experimental configuration. A laser beam (wave vector $\mathbf{k}$) is incident perpendicularly to the long axis of the condensate; its electric-field vector $\mathbf{E}$ is parallel to it and the applied magnetic field $\mathbf{B}$. Each scattering event results in a recoiling atom (momentum $\hslash \mathbf{q}$) and a scattered photon [momentum $\hslash \left(\mathbf{k}-\mathbf{q}\right)$]. The recoiling atoms lie on a shell of radius $\hslash k$. (b) Spontaneous Rayleigh scattering. The absorption image shows a halo of atoms. The intensity of the beam was $1.0\text{mW}∕{\text{cm}}^2$; the pulse duration was $1\text{ms}$. (c) Superradiant Raman scattering as observed for a beam intensity of $18\text{mW}∕{\text{cm}}^2$ and a pulse duration of $100\mu \mathrm{s}$ (the original condensate was fully depleted after $\sim 10\mu \mathrm{s}$. In both cases the field of view was $1.05\times 1.05{\text{mm}}^2$.

Figure 2

Characterization of superradiant Raman scattering. The number of atoms in a single recoil peak is shown for three different situations. (a) Dependence on the pulse duration $\tau$, with constant beam intensity $\left(I=7.6\text{mW}∕{\text{cm}}^2\right)$. The solid line describes an exponential growth according to Eq. (2) with $G-L=(1.7\pm 0.1)\times {10}^5{\mathrm{s}}^{-1}$. (b): Dependence on $\tau$ for a constant gain $G\left(I\tau =140\text{mW}∕{\text{cm}}^2\mu \mathrm{s}\right)$. The atom number decays exponentially with the rate $L=(6.2\pm 0.5)\times {10}^4{\mathrm{s}}^{-1}$ (solid line). (c) Dependence on the laser intensity for a constant pulse duration $\left(\tau =10\mu \mathrm{s}\right)$. The solid line is calculated from Eq. (2) with parameters $L$ and $G∕I=3.0\times {10}^4{\text{cm}}^2∕\text{mW}\mathrm{s}$ as obtained in a and b, predicting a threshold at $2.1\text{mW}∕{\text{cm}}^2$. The open circles represent the measurement of Fig. 4, rescaled for the intensity of the electric-field component along the long axis of the condensate.

Figure 3

(a) Realization of a Raman amplifier for matter waves. The first laser pulse prepares a cloud of $N_q$ recoiling atoms in state $\mid 2⟩$ (input). After a wait time ${\tau }^{\prime }$, these atoms are amplified by a second, identical pulse to a number $N_q^{\prime }=\beta N_q$ (output), where $\beta$ is the amplification factor. (b) and (c) Input and output $(\beta =6)$ for a pulse duration $\tau =1.65\mu \mathrm{s}$ and a wait time ${\tau }^{\prime }=5\mu \mathrm{s}$. The intensity of the laser beam was $60\text{mW}∕{\text{cm}}^2$. The absorption images were taken without optical pumping from $\mid 1⟩$ to $\mid 2⟩$ and therefore do not show the condensate in the center of the field of view. (d) Dependence of the amplification factor $\beta$ on the wait time ${\tau }^{\prime }$. The line represents an exponential decay with a decay rate of $(2.2\pm 0.2)\times {10}^5{\mathrm{s}}^{-1}$.

Figure 4

Tuning between superradiant modes. (a) Raman superradiance (b) Rayleigh superradiance (Kapitza-Dirac regime) for polarization parallel and orthogonal to the condensate axis, respectively. (c) Variation of the atom number in the Raman peaks (open circles) and in the Rayleigh backward peaks (filled circles) with the polarization angle. The angle had a systematic uncertainty of $\sim 10°$ from the orientation of the condensate with respect to the axis of the magnetic trap. The measurements were done for a laser intensity of $12\text{mW}∕{\text{cm}}^2$ and a pulse duration of $10\mu \mathrm{s}$.