Quantum metrology with Dicke squeezed states

Zhang, Zhen; Duan, Luming

doi:10.1088/1367-2630/16/10/103037

Cited by 60 publications

(62 citation statements)

References 30 publications

(71 reference statements)

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“…A clear advantage of using the physical spin is that it is typically much easier to manipulate than the pseudo spin-1 2 particles [33]. In future, it would be interesting to clarify the relation between generalized spin squeezing and metrological usefulness [44][45][46][47][48][49], and also compare our results with the complete set of spin-squeezing criteria of [50], which contain one additional collective observable, related to single-spin average squeezing. and denote its ground state by f l l .…”

Section: Discussionmentioning

confidence: 98%

Entanglement and extreme spin squeezing of unpolarized states

et al. 2017

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We present criteria to detect the depth of entanglement in macroscopic ensembles of spin-j particles using the variance and second moments of the collective spin components. The class of states detected goes beyond traditional spin-squeezed states by including Dicke states and other unpolarized states. The criteria derived are easy to evaluate numerically even for systems of very many particles and outperform past approaches, especially in practical situations where noise is present. We also derive analytic lower bounds based on the linearization of our criteria, which make it possible to define spinsqueezing parameters for Dicke states. In addition, we obtain spin squeezing parameters also from the condition derived in (Sørensen and Mølmer 2001 Phys. Rev. Lett. 86 4431). We also extend our results to systems with fluctuating number of particles. consider a subgroup of  k N particles and define its total spin asWe also need to define a function F J via a minimization over quantum states of such a group aswhere L l are the spin components of the group. In practice, the minimum will be the same if we carry out the minimization over states of a single particle with a spin J [19]. Then, for all pure states with an entanglement depth of at most kholds. It is easy to see that (4) is valid even for mixed states with an entanglement depth of at most k since the variance is concave in the state and F J (X) is convex 5 . Thus, every state that violates (4) must have a depth of entanglement of ( ) + k 1 or larger. It is important to stress that the criterion (4) provides a tight lower bound on ( ) DJ x 2 based on á ñ J .z Spin squeezing has been demonstrated in many experiments, from cold atoms [7, 20-26] to trapped ions [27], magnetic systems [28] and photons [29], and in many of these experiments even multipartite entanglement has been detected using the condition (4) [7,[23][24][25][26]29].Recently, the concept of spin squeezing has been extended to unpolarized states [30][31][32][33][34]. In particular, Dicke states are attracting increasing attention, since their multipartite entanglement is robust against particle loss, and they can be used for high precision quantum metrology [8]. Dicke states are produced in experiments with photons [35,36] and Bose-Einstein condensates [8,37,38]. Suitable criteria to detect the depth of entanglement of Dicke states have also been derived. However, either they are limited to spin-1/2 particles [8,39] or they do not give a tight lower bound on ( ) DJ x 2 based on the expectation value measured for the criterion, concretely,with F J (X) defined as in equation (3) and J = kj as in (2). Our approach is motivated by the fact that equation (4) fails to be a good criterion for mixed states with a low polarization  á ñ + á ñ J J N j y z 2 2 22 . Thus, we consider the second moments á + ñ J J y z 2 2 instead, which are still large for many useful unpolarized quantum states, such as Dicke states. Using the second moments is advantageous even for states with a large spin polarization since c...

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Section: Discussionmentioning

confidence: 98%

Entanglement and extreme spin squeezing of unpolarized states

et al. 2017

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“…That is, while no limitation appears for the case of the CSS thanks to the measurement effect, generating those highly entangled Dicke states is strictly prohibited, irrespective of the use of measurement and control. This result implies that, in practice, there exists a strict limitation in quantum magnetometry that utilizes a highly entangled Dicke state [47]. Another important subject in quantum metrology is the frequency standard, where the GHZ state |GHZ = (|↑ ⊗N + |↓ ⊗N )/ √ 2 is used for estimating the atomic frequency, over the standard quantum limit attained with the use of the product state |+ ⊗N = (|↑ / √ 2 + |↓ / √ 2) ⊗N [48].…”

Section: Atomic Ensemblementioning

confidence: 99%

Control limit on quantum state preparation under decoherence

Kobayashi

Yamamoto

2019

Phys. Rev. A

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Quantum information technologies require careful control for generating and preserving a desired target quantum state. The biggest practical obstacle is, of course, decoherence. Therefore, the reachability analysis, which in our scenario aims to estimate the distance between the controlled state under decoherence and the target state, is of great importance to evaluate the realistic performance of those technologies. This paper presents a lower bound of the fidelity-based distance for a general open Markovian quantum system driven by the decoherence process and several types of control including feedback. The lower bound is straightforward to calculate and can be used as a guide for choosing the target state, as demonstrated in some examples. Moreover, the lower bound is applied to derive a theoretical limit in some quantum metrology problems based on a large-size atomic ensemble under control and decoherence.

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“…Dicke states do not lend themselves well to characterization by conventional spin squeezing measures, which generally rely on a well-defined polarization of the spin state. Instead, to characterize the squeezing we consider the Dicke squeezing parameter [35],…”

Section: Introductionmentioning

confidence: 99%

“…(1) * smas176@aucklanduni.ac.nz † s.parkins@auckland.ac.nz This parameter gives us access to the metrological sensitivity relative to the SQL. For Mach-Zehnder interferometry, the variance is bounded by β(ξ D /N ), where β is a factor of order one [35]. The parameter also provides a lower bound for the entanglement depth of ξ −1 D − 2 [36], where x denotes the minimum integer no less than x.…”

Section: Introductionmentioning

confidence: 99%

Extreme spin squeezing in the steady state of a generalized Dicke model

Masson

Parkins

2019

Phys. Rev. A

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We present a scheme to generate steady-state atomic spin squeezing in a cavity QED system using cavity-mediated Raman transitions to engineer effective atom-photon interactions, which include both linear and nonlinear (dispersive) atom-cavity couplings, on a potentially equal footing. We focus on a regime where the dispersive coupling is very large and find that the steady state of the system can in fact be a strongly spin-squeezed Dicke state, |N/2, 0 , of the atomic ensemble. These states offer Heisenberg-limited metrological properties and feature genuine multipartite entanglement among the entire atomic ensemble.

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Quantum metrology with Dicke squeezed states

Cited by 60 publications

References 30 publications

Entanglement and extreme spin squeezing of unpolarized states

Entanglement and extreme spin squeezing of unpolarized states

Control limit on quantum state preparation under decoherence

Extreme spin squeezing in the steady state of a generalized Dicke model

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