Collective State Measurement of Mesoscopic Ensembles with Single-Atom Resolution

Abstract

We demonstrate single-atom resolution, as well as detection sensitivity more than 20 dB below the quantum projection noise limit, for hyperfine-state-selective measurements on mesoscopic ensembles containing 100 or more atoms. The measurement detects the atom-induced shift of the resonance frequency of an optical cavity containing the ensemble. While spatially-varying coupling of atoms to the cavity prevents the direct observation of a quantized signal, the demonstrated measurement resolution provides the readout capability necessary for atomic interferometry substantially below the standard quantum limit, and down to the Heisenberg limit. PACS numbers:The rapidly progressing field of quantum metrology takes advantage of entangled ensembles of particles to improve measurement sensitivity beyond the standard quantum limit (SQL) arising from quantum projection noise for measurements on uncorrelated particles. Spinsqueezed states [1,2] improve the measurement signalto-noise ratio by redistribution of quantum noise, while GHZ states [3][4][5] enhance the signal via faster-evolving collective phase. GHZ states enable measurement at the Heisenberg limit, where noise-to-signal ratio scales with atom number N as 1/N [5].In both cases, very-high-precision readout is necessary to realize metrological gain. The performance of an entangled interferometer is determined not by the intrinsic fluctuations of the quantum system after detection noise subtraction, but by the full observed noise including detection noise [6][7][8][9][10][11]. Thus, the best observed spin squeezing of 6 dB [7] in a spin-1 2 system, and 8 dB of spin-nematic squeezing in a spin-1 system [11], were both limited by detection. For GHZ states, read-out of the collective phase requires a measurement of the parity of the population difference between two atomic states [5]. A state-selective measurement of atom number with singleatom resolution, which can be used to implement parity detection, therefore represents an important enabling technique for metrology beyond the SQL.An optical cavity can be used both to collect photons in a single mode [12][13][14][15][16][17][18][19][20][21][22], and to generate entangled states via light-mediated atom-atom interactions [7,23,24]. With respect to atom detection, counting of up to 4 atoms [12][13][14][15][16][17][18] and high-fidelity readout of the hyperfine state of a single neutral atom [19][20][21] have been achieved using cavity transmission measurements. Larger ensembles containing up to N = 70 atoms have been measured with atom detection variance (∆N ) 2 = 6 [25]. Spinsqueezed states of atoms in a cavity have also been prepared [7,22,26], and have enabled an atomic clock operating with variance a factor of 3 below the standard quantum limit [27].Single-atom resolution has also been achieved via fluorescence detection in free space. In optical lattices, the parity of site occupation has been measured for up to 5 atoms per lattice site without internal-state discrimination [28][29][30]. For strongly trapped ions...

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

“…Similar to previous work [15,43], we characterize the noise properties of the imaging method by calculating the two-sample variance from the atom number measured by two consecutive imaging pulses:…”

Double-well atom trap for fluorescence detection at the Heisenberg limit

“…Due to light-assisted collisions in the strongly-confining lattice sites, all atom pairs are lost immediately at the outset of the fluorescence detection. Another promising approach is cavity based detection of mesoscopic samples [27], which has shown resolution at the single-atom sensitivity level. Here, however, inhomogeneous coupling of the standing-wave light to the atoms has prevented detection of the exact atom number.…”

Many-atom–cavity QED system with homogeneous atom–cavity coupling

“…Thanks to the homogeneous atom-cavity coupling, the generated squeezed states could be released into free space to be used as input states to atom interferometric sensors for enhanced sensitivity. In addition, the described apparatus might enable atom counting in mesoscopic ensembles with an actual quantized signal, which so far has been challenging [17].…”