In-trap fluorescence detection of atoms in a microscopic dipole trap

We investigate fluorescence detection using a standing wave of blue-detuned light of one or more atoms held in a deep, microscopic dipole trap. The blue-detuned standing wave realizes a Sisyphus laser cooling mechanism so that an atom can scatter many photons while remaining trapped. When imaging more than one atom, the blue detuning limits loss due to inelastic light-assisted collisions. Using this standing-wave probe beam, we demonstrate that we can count from 1 to the order of 100 atoms in the microtrap with sub-Poissonian precision.

Figure 1

Schematic of the experimental setup. ${}^{85}\mathrm{Rb}$ atoms are loaded from a MOT into a microscopic dipole trap. The microtrap is formed by passing 828-nm light through a high-NA lens mounted inside the vacuum chamber. Atoms held in the microtrap are probed by a standing wave of light on the $D_1$ line of ${}^{85}\mathrm{Rb}$. The MOT cooling beams are not shown. A portion of the light scattered by the trapped atoms is detected by an EMCCD camera.

Figure 2

Light shifts for relevant states of ${}^{85}\mathrm{Rb}$ along the radial direction of the microtrap at a power of 20 mW. (a) States addressed by $D_1$ probe beam: ground state $F=2$ (black line) and excited state $F^{\prime }=3$ (red line). The probe-beam optical frequency $\omega$ has been subtracted from the excited-state energy. ${\delta }_{\mathrm{c}}$ is the detuning of the probe beam at the center of the microtrap. Away from the center, an atom experiences a position-dependent detuning $\delta \left(x\right)$ that is larger than ${\delta }_{\mathrm{c}}$. (b) States addressed by the $D_2$ MOT cooling beams: ground state $F=3$ (black line) and excited states $F^{\prime }=3$ (red line) and $F^{\prime }=4$ (blue line). The MOT cooling beams optical frequency ${\omega }_{D_2}$ has been subtracted from the excited-state energies. The magnetic sublevels in the excited states on the $D_2$ line experience different light shifts; the curves show the mean across the magnetic sublevels. ${\delta }_{\mathrm{c}}^{{33}^{\prime }}$ denotes the detuning of the MOT cooling beams from the $F=3\to F^{\prime }=3$ transition on the $D_2$ line at the center of the microtrap, with ${\delta }^{{33}^{\prime }}\left(x\right)$ the position-dependent detuning.

Figure 3

Calculated dressed-state energy for an atom in the microtrap dressed by a standing wave of near-resonant light. The probe beam has power 30 $\mu \mathrm{W}$ and ${\delta }_{\mathrm{c}}=2\pi \times 15$ MHz. The ground state $F=2,m_F=0$ is shifted down by the dipole trap (black dashed line) and modulated by a standing wave of blue-detuned light on the $D_1$ line (black solid line). The excited state $F^{\prime }=3,m_F^{\prime }=0$ is shifted up by the dipole trap (red dashed line) and modulated by the standing wave (red solid line).

Figure 4

(a) Experimental sequence to investigate the fluorescence detection of a single atom. (b) Fluorescence spectrum observed when the probe-beam detuning is varied. Black circles, integrated fluorescence conditioned on the detection of a single atom in the first and third images; red squares, data conditioned only on there being an atom in the first image. Solid lines are fits of asymmetric Lorentzian functions to the data.

Figure 5

Imaging performance as a function of MOT cooling light detuning from $F=3$ to $F^{\prime }=3,{\delta }_{\mathrm{c}}^{{33}^{\prime }}$, at constant MOT cooling light power. The experiment was performed using standing-wave (black circles) and traveling-wave (red squares) probe beams. (a) Probability of retaining an atom in the microtrap. (b) Integrated fluorescence.

Figure 6

Single-atom detection as a function of probe-beam power for three detunings ${\delta }_{\mathrm{c}}=2\pi \times 5$ MHz (black circles), ${\delta }_{\mathrm{c}}=2\pi \times 15$ MHz (red squares), and ${\delta }_{\mathrm{c}}=2\pi \times 35$ MHz (blue diamonds). (a) Probability of retaining an atom in the microtrap. (b) Integrated fluorescence.

Figure 7

Atom number distributions evaluated from Eq. (3) for processes 1 and 2 using $N_0=63,\beta =4.9$ ${\mathrm{s}}^{-1}$, and $\gamma =0.97$ ${\mathrm{s}}^{-1}$. To ensure the same mean atom number for the two processes, we use $\beta$ for process 2 and $2\beta$ for process 1 [see Eq. (4) and associated text]. (a) Mean atom number (black line) calculated from Eq. (4) assuming $\beta \mathrm{\Delta }{N}^2=0$. The shaded regions indicate the $2\sigma$ width of the atom number distributions for processes 2 (gray) and 1 (red). (b) Atom number distribution at 16 ms for process 2. The solid line shows the Poissonian distribution for the mean atom number $\overline{N}=10.6$. (c) Same as (b) but for process 1.

Figure 8

(a) Experimental timeline for multiatom detection. (b) Integrated fluorescence as a function of exposure time for three values of the initial atom number $N_0$. Each data set was fitted with Eq. (7) using $F_1$ and $\gamma$ as fixed input parameters (see text). The fitted parameters were as follows: (black circles) $N_0=85.9\left(5\right),\beta =6.41\left(4\right){\mathrm{s}}^{-1}$; (red squares) $N_0=58.4\left(4\right),\beta =6.00\left(5\right){\mathrm{s}}^{-1}$; (blue diamonds) $N_0=31.3\left(3\right),\beta =5.70\left(9\right){\mathrm{s}}^{-1}$. The number in parentheses gives the uncertainty from the fitting routine in the least significant figure.

Figure 9

(a) Measured atom number at the end of pulse 1 and 2 for three imaging pulse durations: $\tau =0.1$ ms (black circles), $\tau =1$ ms (red squares), $\tau =3$ ms (blue diamonds). The dashed line shows $N_2=N_1$. (b) Same as (a), but we compare the atom number at the end of the first pulse $N_1$ and the number at the beginning at the second pulse $N_2^0$ inferred from the second pulse.

Figure 10

(a) Two-sample variance of $N_1$ and $N_2$ as a function of exposure time. (Black circles) Experimental data, error bars show $2\sigma$ statistical error, (red dash-dotted line) calculated light noise ${\sigma }_{N_1}^2+{\sigma }_{N_2}^2$, (blue dotted line) calculated noise arising from atom loss ${\sigma }_{\mathrm{loss}}^2$ based on Eq. (3) using process 1, (black solid line) calculated total noise ${\sigma }^2={\sigma }_{N_1}^2+{\sigma }_{N_2}^2+{\sigma }_{\mathrm{loss}}^2$ using process 1, (green dashed line) calculated total noise model using process 2. The shaded region indicates the interval where the atom number variance lies below the level of Poissonian fluctuations. (b) Same as (a), but for $N_1$ and $N_2^0$.