Mesoscopic atomic entanglement for precision measurements beyond the standard quantum limit

Appel, J.; Windpassinger, Patrick; Oblak, Daniel; Hoff, Ulrich Busk; Kjærgaard, Niels; Polzik, E. S.

doi:10.1073/pnas.0901550106

Cited by 380 publications

(458 citation statements)

References 34 publications

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“…In the atomic literature, where |a and |b refer to different atomic levels, |ψ (N) 0 often is referred to as "spin-squeezed state" [42,43] or "Schrödinger-cat state" [44][45][46]. It has been experimentally demonstrated using trapped ions [44][45][46][47], Bose-Einstein condensates [48], macroscopic atomic ensembles [49], and NMR [50]. 5 The map Φx is called programmable if one can express it in terms of a constant interaction with an external ancillary system B whose initial state encodes the dependence on the parameter x, i.e.…”

Section: Quantum Parameter Estimation For Channelsmentioning

confidence: 99%

Advances in quantum metrology

2011

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In classical estimation theory, the central limit theorem implies that the statistical error in a measurement outcome can be reduced by an amount proportional to n −1/2 by repeating the measures n times and then averaging. Using quantum effects, such as entanglement, it is often possible to do better, decreasing the error by an amount proportional to n −1 . Quantum metrology is the study of those quantum techniques that allow one to gain advantages over purely classical approaches.In this review, we analyze some of the most promising recent developments in this research field. Specifically, we deal with the developments of the theory and point out some of the new experiments. Then we look at one of the main new trends of the field, the analysis of how the theory must take into account the presence of noise and experimental imperfections.Any measurement consists in three parts: the preparation of a probe, its interaction with the system to be measured, and the probe readout. This process is often plagued by statistical or systematic errors. The source of the former can be accidental (e.g. deriving from an insufficient control of the probes or of the measured system) or fundamental (e.g. deriving from the Heisenberg uncertainty relations). Whatever their origin, we can reduce their effect by repeating the measurement and averaging the resulting outcomes. This is a consequence of the central-limit theorem: given a large number n of independent measurement results (each having a standard deviation ∆σ), their average will converge to a Gaussian distribution with standard deviation ∆σ/ √ n, so that the error scales as n −1/2 . In quantum mechanics this behavior is referred to as "standard quantum limit" (SQL) and is associated with procedures which do not fully exploit the quantum nature of the system under investigation 1 . Notably it is possible to do better when one employs quantum effects, such as entanglement among the probing devices employed for the measurements, e.g. see Refs. [1][2][3][4][5][6]. Consequently, the SQL is not a fundamental quantum mechanical bound as it can be surpassed by using "non-classical" strategies. Nonetheless, through Heisenberg-like uncertainty relations, quantum mechanics still sets ultimate limits in precision which are typically referred to as "Heisenberg bounds". In Fig. 1 we present a simple example which may be useful to un-1 In quantum optics, the n −1/2 scaling is also indicated as "shot noise", since it is connected to the discrete nature of the radiation that can be heard as "shots" in a photon counter operating in Geiger mode.derstand the quantum enhancement. Part of the emerging field of quantum technology [7], quantum metrology studies these bounds and the (quantum) strategies which allows us to attain them. More generally it deals with measurement and discrimination procedures that receive some kind of enhancement (in precision, efficiency, simplicity of implementation, etc.) through the use of quantum effects. This paper aims to review some of the most recent developmen...

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Section: Quantum Parameter Estimation For Channelsmentioning

confidence: 99%

Advances in quantum metrology

2011

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“…Such counting has been used to generate highly spin-squeezed states [1,24] that surpass the standard quantum limit on phase estimation [25][26][27]. More simply, but quite importantly, non-destructive readout methods [28] can reduce the highly deleterious effects of local oscillator noise aliasing [29,30] in optical lattice clocks.…”

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confidence: 99%

Strong coupling on a forbidden transition in strontium and nondestructive atom counting

Norcia

Thompson

2016

Phys. Rev. A

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We observe strong collective coupling between an optical cavity and the forbidden spin singlet to triplet optical transition 1 S0 to 3 P1 in an ensemble of 88 Sr. Despite the transition being 1000 times weaker than a typical dipole transition, we observe a well resolved vacuum Rabi splitting. We use the observed vacuum Rabi splitting to make non-destructive measurements of atomic population with the equivalent of projection-noise limited sensitivity and minimal heating (< 0.01 photon recoils/atom). This technique may be used to enhance the performance of optical lattice clocks by generating entangled states and reducing dead time.Two modes are strongly coupled when the frequency Ω at which they exchange excitations exceeds the rate of interaction with the environment. Strong coupling enables one to generate large amounts of entanglement [1, 2], achieve efficient quantum memories [3], cool the motion of atoms [4] and mesoscopic oscillators [5], and explore collective self-organization and synchronization phenomena such as superradiant lasing [6][7][8][9] and the Dicke phase transition [10,11].In this Letter, we observe strong coupling between an optical cavity and the collective excitation of up to N = 1.25 × 10 5 strontium atoms in a 1D optical lattice. The strong coupling is achieved using the forbidden electronic spin singlet to triplet optical transition 1 S 0 to 3 P 1 in 88 Sr. The excited state 3 P 1 couples to the environment via spontaneous emission at the relatively slow rate of γ = 2π × 7.5 kHz.Despite operating on a transition with 1000 times smaller squared matrix element than transitions typically used in optical cavity-QED experiments, we observe a highly-resolved splitting of the normal modes of the coupled atom-cavity system, known as a collective vacuum Rabi splitting [12,13]. This observation demonstrates that despite the relative feebleness of the transition, the tools of cavity-QED can now be applied to a system of extreme interest for quantum metrology [14]. Example technologies include optical lattice clocks [15][16][17] and ultra-narrow lasers [6][7][8][9], along with their associated broad range of potential applications such defining the second [14,18], quantum many-body simulations [19], measuring gravitational potentials [20] and gravity waves [21], and searches for physics beyond the standard model [22,23].One relevant application of this newly achieved regime is for state-selective, non-destructive counting of strontium atoms. Such counting has been used to generate highly spin-squeezed states [1,24] that surpass the standard quantum limit on phase estimation [25][26][27]. More simply, but quite importantly, non-destructive readout methods [28] can reduce the highly deleterious effects of local oscillator noise aliasing [29,30] in optical lattice clocks. Here, we utilize the observed vacuum Rabi splitting to non-destructively count atoms with the equivalent of sub-projection noise sensitivity. We verify that this sensitivity is achieved with as few as 0.01 photon recoils imparted to e...

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“…In the next step, we replace the spin coherent state with a spin-squeezed state which has reduced fluctuations of the relative atom number between the two modes [6][7][8][9][10][11][12]. Such a state is characterized with the spin-squeezing parameter [4,5] …”

Section: Ultimate Precision -Quantum Fisher Informationmentioning

confidence: 99%

“…Spin-squeezed states (ξ 2 n < 1) are particle-entangled and potentially useful for quantum metrology. Recently, the spin-squeezing has been generated in two-mode quantum systems [6][7][8][9][10][11][12]. A similar technique to detect the nonclassical correlations was used in a collection of atoms scattered from a single Bose-Einstein condensate in the spin-changing collisions [13].…”

Section: Introductionmentioning

confidence: 99%

Atom interferometer in a double-well potential

Gietka

Chwedeńczuk

2014

Phys. Rev. A

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We present a detailed study of an atom interferometer which can be realized in a double-well potential. We assume that the interferometric phase is imprinted in the presence of coherent tunneling between the wells. We calculate the ultimate bounds for the estimation sensitivity and show how they relate to the precision of the Mach-Zehnder interferometer. The interferometer presented here allows for sub shot-noise sensitivity when fed with the spin-squeezed states with reduced either the relative population imbalance or the relative phase. We also calculate the precision of the estimation from the population imbalance and show that it overcomes the shot-noise level when the entangled squeezed-states are used at the input.

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Mesoscopic atomic entanglement for precision measurements beyond the standard quantum limit

Cited by 380 publications

References 34 publications

Advances in quantum metrology

Advances in quantum metrology

Strong coupling on a forbidden transition in strontium and nondestructive atom counting

Atom interferometer in a double-well potential

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