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arXiv:1410.2268 · Physical Review A

N−atom collective-state atomic clock with N−fold increase in effective frequency and N−fold reduction in fringe width

May E. Kim, Resham Sarkar, Renpeng Fang, M. S. Shahriar

Published Jun 24, 2015• 6 citations
arXivHTMLPDF

Abstract

We describe a collective state atomic clock (COSAC) with Ramsey fringes narrowed by a factor of $\sqrt{N}$ compared to a conventional clock---$N$ being the number of noninteracting atoms---without violating the uncertainty relation. This narrowing is explained as being due to interferences among the collective states, representing an effective $\sqrt{N}$-fold increase in the clock frequency, without entanglement. We discuss the experimental inhomogeneities that affect the signal and show that experimental parameters can be adjusted to produce a near ideal signal. The detection process collects fluorescence through stimulated Raman scattering of Stokes photons, which emits photons predominantly in the direction of the probe beam for a high enough optical density. By using a null measurement scheme, in which detection of zero photons corresponds to the system being in a single collective state, we detect the population in a collective state of interest. The quantum and classical noise of the ideal COSAC is still limited by the standard quantum limit and performs only as well as the conventional clock. However, when detection efficiency and collection efficiency are taken into account, the detection scheme of the COSAC increases the quantum efficiency of detection significantly in comparison to a typical conventional clock employing fluorescence detection, yielding a net improvement in stability by as much as a factor of 10.

DOI
10.1103/physreva.91.063629

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We describe a collective state atomic clock (COSAC) with Ramsey fringes narrowed by a factor of N\sqrt{N}N​ compared to a conventional clock---NNN being the number of noninteracting atoms---without violating the uncertainty relation. This narrowing is explained as being due to interferences among the collective states, representing an effective N\sqrt{N}N​-fold increase in the clock frequency, without entanglement. We discuss the experimental inhomogeneities that affect the signal and show that experimental parameters can be adjusted to produce a near ideal signal. The detection process collects fluorescence through stimulated Raman scattering of Stokes photons, which emits photons predominantly in the direction of the probe beam for a high enough optical density. By using a null measurement scheme, in which detection of zero photons corresponds to the system being in a single collective state, we detect the population in a collective state of interest. The quantum and classical noise of the ideal COSAC is still limited by the standard quantum limit and performs only as well as the conventional clock. However, when detection efficiency and collection efficiency are taken into account, the detection scheme of the COSAC increases the quantum efficiency of detection significantly in comparison to a typical conventional clock employing fluorescence detection, yielding a net improvement in stability by as much as a factor of 10.
We describe a collective-state atomic interferometer (COSAIN) with the signal fringe as a function of phase difference or rotation narrowed by N\sqrt{N}N​ compared to a conventional interferometer, NNN being the number of atoms, without entanglement. This effect arises from the interferences among collective states, and is a manifestation of interference at a Compton frequency of $10\phantom{\rule{0.16em}{0ex}}\ifmmode\times\else\texttimes\fi{}\phantom{\rule{0.16em}{0ex}}{10}^{30}$ Hz, or a de Broglie wavelength of 4.5 femtometer, for N=106N={10}^{6}N=106 and v=1v=1v=1 m/s. The population of the collective state of interest is detected by a null measurement scheme, in which an event corresponding to detection of zero photons corresponds to the system being in that particular collective state. The signal is detected by collecting fluorescence through stimulated Raman scattering of Stokes photons, which are emitted predominantly against the direction of the probe beam, for a high enough resonant optical density. The sensitivity of the ideal COSAIN is found to be given by the standard quantum limit. However, when detection efficiency and collection efficiency are taken into account, the detection scheme of the COSAIN increases the quantum efficiency of detection significantly in comparison to a typical conventional Raman atomic interferometer employing fluorescence detection, yielding a net improvement in stability by as much as a factor of 10. We discuss how the inhomogeneities arising from the nonuniformity in experimental parameters affect the COSAIN signal. We also describe an alternate experimental scheme to enhance resonant optical density in a COSAIN by using cross-linearly polarized counterpropagating Raman beams.
In a conventional atomic interferometer employing NNN atoms, the phase sensitivity is at the standard quantum limit: 1/N1/\sqrt{N}1/N​. Using spin-squeezing, the sensitivity can be increased, either by lowering the quantum noise or via phase amplification, or a combination thereof. Here, we show how to increase the sensitivity, to the Heisenberg limit of 1/N1/N1/N, while increasing the quantum noise by N\sqrt{N}N​, thereby suppressing by the same factor the effect of excess noise. The protocol uses a Schrodinger Cat state representing a superposition of two collective states of NNN atoms, behaving as a single entity with an NNN-fold increase in Compton frequency. The resulting NNN-fold phase magnification is revealed by using atomic state detection instead of collective state detection. We also show how to realize an atomic clock based on such a Schrodinger Cat state, with an NNN-fold increase in the effective transition frequency. We discuss potential experimental constraints for implementing this scheme, using one axis twist squeezing employing the cavity feedback scheme, and show that the effects of cavity decay and spontaneous emission are highly suppressed. We find that the maximum improvement in sensitivity can be close to the ideal limit, for as many as ten million atoms.
In a conventional atomic interferometer employing NNN atoms, the phase sensitivity is at the standard quantum limit: 1/N1/\sqrt{N}1/N​. Using spin-squeezing, the sensitivity can be increased, either by lowering the quantum noise or via phase amplification, or a combination thereof. Here, we show how to increase the sensitivity, to the Heisenberg limit of 1/N1/N1/N, while increasing the quantum noise by N\sqrt{N}N​, thereby suppressing by the same factor the effect of excess noise. The protocol uses a Schrodinger Cat state representing a superposition of two collective states of NNN atoms, behaving as a single entity with an NNN-fold increase in Compton frequency. The resulting NNN-fold phase magnification is revealed by using atomic state detection instead of collective state detection. We also show how to realize an atomic clock based on such a Schrodinger Cat state, with an NNN-fold increase in the effective transition frequency. We discuss potential experimental constraints for implementing this scheme, using one axis twist squeezing employing the cavity feedback scheme, and show that the effects of cavity decay and spontaneous emission are highly suppressed. We find that the maximum improvement in sensitivity can be close to the ideal limit, for as many as ten million atoms.
The precision of an atomic clock based on the standard Ramsey spectroscopy, involving the measurement of the population of the atomic excited state, essentially a measurement of energy, is determined by the free evolution time T between successive /2 pulses. The longer the time T, the narrower the Ramsey interference fringes and thus the greater the precision. The stability of an atomic clock is also increased with increased T. But there are practical limits to the degree to which T can be extended. The main approach so far has been through the introduction of the so-called atomic fountain clocks. In this talk we present alternative approach not based on extending T but based on collective atomic states where a non-classical observable, an observable having no classical counterpart, is to be measured. This is the collective atomic, or SU(2), parity for an ensemble of two-level atoms. We show that with this observable the corresponding Ramsey-like fringes can become remarkably narrower with an increasing number of atoms in the ensemble even when the atomics are not prepared in an entangled state. By preparing the atoms in an entangled state, such as a state known to be spin-squeezed, the precision can be further increased through atomic parity measurements. The issue of performing the required collective atomic parity measurements will be discussed.
Ramsey interferometry is routinely used in quantum metrology for the most sensitive measurements of optical clock frequencies. Spontaneous decay to the electromagnetic vacuum ultimately limits the interrogation time and thus sets a lower bound to the optimal frequency sensitivity. In dense ensembles of two-level systems, the presence of collective effects such as superradiance and dipole-dipole interaction tends to decrease the sensitivity even further. We show that by a redesign of the Ramsey-pulse sequence to include different rotations of individual spins that effectively fold the collective state onto a state close to the center of the Bloch sphere, partial protection from collective decoherence is possible. This allows a significant improvement in the sensitivity limit of a clock transition detection scheme over the conventional Ramsey method for interacting systems and even for noninteracting decaying atoms.