Abstract: We analyze a proposed experiment [Boixo et al., Phys. Rev. Lett. 101, 040403 (2008)] for achieving sensitivity scaling better than 1/N in a nonlinear Ramsey interferometer that uses a two-mode Bose-Einstein condensate (BEC) of N atoms. We present numerical simulations that confirm the analytical predictions for the effect of the spreading of the BEC ground-state wave function on the ideal 1/N^(3/2) scaling. Numerical integration of the coupled, time-dependent, two-mode Gross-Pitaevskii equations allows us to study the several simplifying assumptions made in the initial analytic study of the proposal and to explore when they can be justified. In particular, we find that the two modes share the same spatial wave function for a length of time that is sufficient to run the metrology scheme.

Publication: Physical Review A Vol.: 82 No.: 5 ISSN: 1050-2947

ID: CaltechAUTHORS:20110302-105500266

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Abstract: We discuss a quantum-metrology protocol designed to estimate a physical parameter in a Bose-Einstein condensate of N atoms, and we show that the measurement uncertainty can decrease faster than 1/N. The 1/N scaling is usually thought to be the best possible in any measurement scheme. From the perspective of quantum information theory, we outline the main idea that leads to a measurement uncertainty that scales better than 1/N. We examine in detail some potential problems and challenges that arise in implementing such a measurement protocol using a Bose-Einstein condensate. We discuss how some of these issues can be dealt with by using lower-dimensional condensates trapped in nonharmonic potentials.

Publication: Physical Review A Vol.: 80 No.: 3 ISSN: 1050-2947

ID: CaltechAUTHORS:20091021-112848560

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Abstract: Questions about quantum limits on measurement precision were once viewed from the perspective of how to reduce or avoid the effects of quantum noise. With the advent of quantum information science came a paradigm shift to proving rigorous bounds on measurement precision. These bounds have been interpreted as saying, first, that the best achievable sensitivity scales as 1/n, where n is the number of particles one has available for a measurement and, second, that the only way to achieve this Heisenberg-limited sensitivity is to use quantum entanglement. We review these results and show that using quadratic couplings of n particles to a parameter to be estimated, one can achieve sensitivities that scale as 1/n^2 if one uses entanglement, but even in the absence of any entanglement at any time during the measurement protocol, one can achieve a super-Heisenberg scaling of 1/n^(3/2)

No.: 1110
ID: CaltechAUTHORS:20100511-100311769

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Abstract: We show how a generalized quantum metrology protocol can be implemented in a two-mode Bose-Einstein condensate of n atoms, achieving a sensitivity that scales better than 1/n and approaches 1/n^(3/2) for appropriate design of the condensate.

Publication: AIP Conference Proceedings No.: 1110 ISSN: 0094-243X

ID: CaltechAUTHORS:20100510-121135555

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Abstract: We propose a communication-assisted local-hidden-variable model that yields the correct outcome for the measurement of any product of Pauli operators on an arbitrary graph state, i.e., that yields the correct global correlation among the individual measurements in the Pauli product. Within this model, communication is restricted to a single round of message passing between adjacent nodes of the graph. We show that any model sharing some general properties with our own is incapable, for at least some graph states, of reproducing the expected correlations among all subsets of the individual measurements. The ability to reproduce all such correlations is found to depend on both the communication distance and the symmetries of the communication protocol.

Publication: Physical Review A Vol.: 75 No.: 1 ISSN: 1050-2947

ID: CaltechAUTHORS:BARpra07

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Abstract: In a recent paper, Deutsch claims to derive the ‘probabilistic predictions of quantum theory’ from the ‘non–probabilistic axioms of quantum theory’ and the ‘nonprobabilistic part of classical decision theory.’ We show that his derivation includes a crucial hidden assumption that vitiates the force of his argument. Furthermore, we point out that in classical decision theory a standard set of non–probabilistic axioms is already sufficient to endow possible outcomes with a natural probability structure. Within that context we argue that Gleason's theorem, relying on fewer assumptions than Deutsch, provides a compelling derivation of the quantum probability law.

Publication: Proceedings of the Royal Society A: Mathematical, physical, and engineering sciences Vol.: 456 No.: 1997 ISSN: 1364-5021

ID: CaltechAUTHORS:20201215-170631438

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Abstract: A laser's intensity can be stabilized by negative feedback from a conventional photodetector. I propose extraction of sub-shot-noise light from the feedback loop at a beam splitter by illuminating the back side of the beam splitter with squeezed-state light.

Publication: Optics Letters Vol.: 12 No.: 11 ISSN: 0146-9592

ID: CaltechAUTHORS:CAVol87

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Abstract: We develop a wideband traveling-wave formalism for analyzing quantum mechanically a degenerate parametric amplifier. The formalism is based on spatial differential equations-spatial Langevin equations-that propagate temporal Fourier components of the field operators through the nonlinear medium. In addition to the parametric nonlinearity, the Langevin equations include absorption and associated fluctuations, dispersion (phase mismatching), and pump quantum fluctuations. We analyze the dominant effects of phase mismatching and pump quantum fluctuations on the squeezing produced by a degenerate parametric amplifier.

Publication: Journal of the Optical Society of America B Vol.: 4 No.: 10 ISSN: 0740-3224

ID: CaltechAUTHORS:CAVjosab87

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Abstract: The monitoring of a quantum-mechanical harmonic oscillator on which a classical force acts is important in a variety of high-precision experiments, such as the attempt to detect gravitational radiation. This paper reviews the standard techniques for monitoring the oscillator, and introduces a new technique which, in principle, can determine the details of the force with arbitrary accuracy, despite the quantum properties of the oscillator. The standard method for monitoring the oscillator is the "amplitude-and-phase" method (position or momentum transducer with output fed through a narrow-band amplifier). The accuracy obtainable by this method is limited by the uncertainty principle ("standard quantum limit"). To do better requires a measurement of the type which Braginsky has called "quantum nondemolition." A well known quantum nondemolition technique is "quantum counting," which can detect an arbitrarily weak classical force, but which cannot provide good accuracy in determining its precise time dependence. This paper considers extensively a new type of quantum nondemolition measurement—a "back-action-evading" measurement of the real part X_1 (or the imaginary part X_2) of the oscillator's complex amplitude. In principle X_1 can be measured "arbitrarily quickly and arbitrarily accurately," and a sequence of such measurements can lead to an arbitrarily accurate monitoring of the classical force. The authors describe explicit Gedanken experiments which demonstrate that X_1 can be measured arbitrarily quickly and arbitrarily accurately. In these experiments the measuring apparatus must be coupled to both the position (position transducer) and the momentum (momentum transducer) of the oscillator, and both couplings must be modulated sinusoidally. For a given measurement time the strength of the coupling determines the accuracy of the measurement; for arbitrarily strong coupling the measurement can be arbitrarily accurate. The "momentum transducer" is constructed by combining a "velocity transducer" with a "negative capacitor" or "negative spring." The modulated couplings are provided by an external, classical generator, which can be realized as a harmonic oscillator excited in an arbitrarily energetic, coherent state. One can avoid the use of two transducers by making "stroboscopic measurements" of X_1, in which one measures position (or momentum) at half-cycle intervals. Alternatively, one can make "continuous single-transducer" measurements of X_1 by modulating appropriately the output of a single transducer (position or momentum), and then filtering the output to pick out the information about X_1 and reject information about X_2. Continuous single-transducer measurements are useful in the case of weak coupling. In this case long measurement times are required to achieve good accuracy, and continuous single-transducer measurements are almost as good as perfectly coupled two-transducer measurements. Finally, the authors develop a theory of quantum nondemolition measurement for arbitrary systems. This paper (Paper I) concentrates on issues of principle; a sequel (Paper II) will consider issues of practice.

Publication: Reviews of Modern Physics Vol.: 52 No.: 2 ISSN: 0034-6861

ID: CaltechAUTHORS:20120719-163130442

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Abstract: The complex amplitude X1+iX2≡(x+ip / mω)e^(iωt) of a harmonic oscillator is constant in the absence of driving forces. Although the uncertainty principle forbids precise measurements of X1 and X2 simultaneously (ΔX1ΔX2>~ℏ / 2mω), X1 alone can be measured precisely and continuously ("quantum nondemolition measurement"). Examples are given of measuring systems that do this job. Such systems might play a crucial role in gravitational-wave detection and elsewhere.

Publication: Physical Review Letters Vol.: 40 No.: 11 ISSN: 0031-9007

ID: CaltechAUTHORS:THOprl78

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Abstract: Advancing technology will soon make possible a new class of gravitation experiments: pure laboratory experiments with laboratory sources of non-Newtonian gravity and laboratory detectors. This paper proposes seven such experiments; and for each one it describes, briefly, the dominant sources of noise and the technology required. Three experiments would utilize a high-Q torque balance as the detector. They include (i) an "Ampère-type" experiment to measure the gravitational spin-spin coupling of two rotating bodies, (ii) a search for time changes of the gravitation constant, and (iii) a measurement of the gravity produced by magnetic stresses and energy. Three experiments would utilize a high-Q dielectric crystal as the detector. They include (i) a "Faraday-type" experiment to measure the "electric-type" gravity produced by a time-changing flux of "magnetic-type" gravity, (ii) a search for "preferred-frame" and "preferred-orientation" effects in gravitational coupling, and (iii) a measurement of the gravitational field produced by protons moving in a storage ring at nearly the speed of light. One experiment would use a high-Q toroidal microwave cavity as detector to search for the dragging of inertial frames by a rotating body.

Publication: Physical Review D Vol.: 15 No.: 8 ISSN: 2470-0010

ID: CaltechAUTHORS:BRAprd77

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