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arXiv:1809.00014 · Physical Review A

Statistical sensitivity of phase measurements via laser-induced fluorescence with optical cycling detection

Zack Lasner, David P. DeMille

Published Nov 14, 2018• 19 citations
arXivHTMLPDF

Abstract

In atomic and molecular phase measurements using laser-induced fluorescence detection, optical cycling can enhance the effective photon detection efficiency and hence improve sensitivity. We show that detecting many photons per atom or molecule, while necessary, is not a sufficient condition to approach the quantum projection limit for detection of the phase in a two-level system. In particular, detecting the maximum number of photons from an imperfectly closed optical cycle reduces the signal-to-noise ratio (SNR) by a factor of $\sqrt{2}$, compared to the ideal case in which leakage from the optical cycle is sufficiently small. We derive a general result for the SNR in a system in terms of the photon detection efficiency, probability for leakage out of the optical cycle per scattered photon, and the product of the average photon scattering rate and total scattering time per atom or molecule.

DOI
10.1103/physreva.98.053823

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•Dec 13, 2018•0 citations
In atomic and molecular phase measurements using laser-induced fluorescence detection, optical cycling can enhance the effective photon detection efficiency and hence improve sensitivity. We show that detecting many photons per atom or molecule, while necessary, is not a sufficient condition to approach the quantum projection limit for detection of the phase in a two-level system. In particular, detecting the maximum number of photons from an imperfectly closed optical cycle reduces the signal-to-noise ratio (SNR) by a factor of 2\sqrt{2}2​, compared to the ideal case in which leakage from the optical cycle is sufficiently small. We derive a general result for the SNR in a system in terms of the photon detection efficiency, probability for leakage out of the optical cycle per scattered photon, and the product of the average photon scattering rate and total scattering time per atom or molecule.
Interferometric detection of gravitational waves at a level of astrophysical interest is expected to require measurement of optical phase differences of < or = 10(-10) rad. A fundamental limit to the phase sensing is the statistics of photon detection--Poisson statistics for light in a coherent state. We have built a laboratory-scale interferometer to achieve and investigate the phase detection sensitivity required for the Laser Interferometer Gravitational-Wave Observatory. With 70 W of circulating power, we have obtained a phase sensitivity of 1.28 x 10(-10) rad/square root(Hz) at frequencies above 600 Hz, limited by quantum noise. Below 600 Hz, excess noise above the quantum limit is seen, and we present our investigations into the sources of this excess. Compared with the results of previous such experiments, the phase sensitivity over the full 100-Hz-10-kHz band of interest has been improved by factors of up to 100, with a factor-of-2.5 improvement in the quantum-limited level.
The classically defined minimum uncertainty of the optical phase is known as the standard quantum limit or shot-noise limit (SNL), originating in the uncertainty principle of quantum mechanics. Based on the SNL, the phase sensitivity is inversely proportional to K, where K is the number of interfering photons or statistically measured events. Thus, using a high-power laser is advantageous to enhance sensitivity due to the K gain in the signal-to-noise ratio. In a typical interferometer, however, the resolution remains in the diffraction limit of the K = 1 case unless the interfering photons are resolved as in quantum sensing. Here, a projection measurement method in quantum sensing is adapted for classical sensing to achieve an additional K gain in the resolution. To understand the projection measurements, several types of conventional interferometers based on N-wave interference are coherently analyzed as a classical reference and numerically compared with the proposed method. As a result, the Kth-order intensity product applied to the N-wave spectrometer exceeds the diffraction limit in classical sensing and the Heisenberg limit in quantum sensing, where the classical N-slit system inherently satisfies the Heisenberg limit of π/N in resolution.
We demonstrate that there is a fundamental limit to the sensitivity of phase-based detection of atoms with light for a given maximum level of allowable spontaneous emission. This is a generalization of previous results for two- and three-level atoms. The limit is due to an upper bound on the phase shift that can be imparted on a laser beam for a given excited-state population. Specifically, we show that no single-pass optical technique using classical light, based on any number of lasers or coherences between any number of levels, can exceed the limit imposed by the two-level atom. This puts significant restrictions on potential nondestructive optical measurement schemes.
We demonstrate a quasioptical cycling for the $X(v=0)\ensuremath{\rightarrow}A({v}^{\ensuremath{'}}=0)$ transition and a radiative force-induced deflection on the buffer-gas-cooled BaF molecular beam. The laser-induced fluorescence enhancement with additional sidebands and a polarization modulation scheme indicates that the hyperfine states and the Zeeman sublevels are closed. The quasioptical cycling by repumping the $X(v=1)\ensuremath{\rightarrow}A({v}^{\ensuremath{'}}=0)$ leads to an $\ensuremath{\sim}0.8\ensuremath{-}\mathrm{mm}$ deflection of the beam via scattering $\ensuremath{\sim}150$ photons per molecule, in good agreement with the predictions from our multilevel rate equation model. Further improvement by closing the leakage X(v=2)X(v=2)X(v=2) and $\mathrm{\ensuremath{\Delta}}$ state allows scattering of thousands of photons and laser cooling and slowing of BaF.
We measure phase-dependent fluorescence spectra for an elementary system: long-lived coherently driven two-level atoms in an atomic beam. Phase-dependent fluorescence spectra measure quadrature noise in the atomic radiation field. These noise spectra are obtained using a homodyne detection scheme that suppresses excess noise by subtracting signals from two identically prepared atomic samples. Noise spectra are obtained for atomic radiation which is in phase $(0\ifmmode^\circ\else\textdegree\fi{})$ and out of phase $(90\ifmmode^\circ\else\textdegree\fi{})$ with a resonant driving field, as well as $\ifmmode\pm\else\textpm\fi{}45\ifmmode^\circ\else\textdegree\fi{}$ out of phase with an off-resonant driving field. The measured phase-dependent fluorescence spectra are much richer than ordinary fluorescence spectra, and exhibit many novel features. Particularly interesting are phase-dependent noise spectra for off-resonant excitation. These strikingly exhibit direct manifestations of time ordering, which appear as large differences between the measured $45\ifmmode^\circ\else\textdegree\fi{}$ and $\ensuremath{-}45\ifmmode^\circ\else\textdegree\fi{}$ quadrature noise spectra. The measured noise spectra are in excellent agreement in magnitude and shape with the results of a quantum treatment using no free parameters.
The work achieved in the frame of this PhD training consisted in the implementation of a cavity enhanced non destructive detection system of atoms trapped in an optical lattice aiming at improving the stability of an optical strontium clock.The characterization of the system in its classical regime, for which a sufficiently low number of photons are scattered per atom to avoid expelling them off the trap, highlighted significant improvements in term of signal to noise ratio, with gain factor around 100 compared with the previously used fluorescence scheme. Yet, gains in terms of stability via Dick effect reduction still have to be demonstrated.Regarding the quantum regime, for which less than one photon is scattered per atom over the detection, new ideas and significant changes have been carried out on the system and a theoretical study was has been undertaken to determine the strategy for the improvement of the clock stability by quantum projection noise reduction via quantum non demolition measurement.It was as well the opportunity to study the effect of the hot collisions between the trapped strontium atoms and the residual vacuum background gas particles, allowing for the improvement of the clock uncertainty. This work reports in particular on the first measurement of strontium clock hot collisions shifts as well as its theoretical study.