Entanglement and Extreme Spin Squeezing

Sørensen, Anders S.; Mølmer, Klaus

doi:10.1103/physrevlett.86.4431

Cited by 426 publications

(609 citation statements)

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“…While prior to this work a negative Wigner function had not been attained for atomic ensembles, in the optical domain, a negativevalued Wigner function has very recently been measured for states with up to 110 microwave photons [18]. Another entanglement measure is the entanglement depth [19], i.e. the minimum number of atoms that are demonstrably, but possibly weakly, entangled with one another.…”

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confidence: 99%

Entanglement with negative Wigner function of almost 3,000 atoms heralded by one photon

McConnell

Zhang

et al. 2015

Nature

212

218

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Quantum-mechanically correlated (entangled) states of many particles are of interest in quantum information, quantum computing and quantum metrology. Metrologically useful entangled states of large atomic ensembles have been experimentally realized [1][2][3][4][5][6][7][8][9][10], but these states display Gaussian spin distribution functions with a non-negative Wigner function. Non-Gaussian entangled states have been produced in small ensembles of ions [11,12], and very recently in large atomic ensembles [13][14][15]. Here, we generate entanglement in a large atomic ensemble via the interaction with a very weak laser pulse; remarkably, the detection of a single photon prepares several thousand atoms in an entangled state. We reconstruct a negative-valued Wigner function, an important hallmark of nonclassicality, and verify an entanglement depth (minimum number of mutually entangled atoms) of 2910 ± 190 out of 3100 atoms. This is the first time a negative Wigner function or the mutual entanglement of virtually all atoms have been attained in an ensemble containing more than a few particles. While the achieved purity of the state is slightly below the threshold for entanglement-induced metrological gain, further technical improvement should allow the generation of states that surpass this threshold, and of more complex Schrödinger cat states for quantum metrology and information processing. More generally, our results demonstrate the power of heralded methods for entanglement generation, and illustrate how the information contained in a single photon can drastically alter the quantum state of a large system.Entanglement is now recognized as a resource for secure communication, quantum information processing, and precision measurements. An important goal is the creation of entangled states of many-particle systems while retaining the ability to characterize the quantum state and validate entanglement. Entanglement can be verified in a variety of ways, with one of the strictest criteria being a negative-valued Wigner function [16,17], that necessarily implies that the entangled state has a non-Gaussian wavefunction. To date, the metrologically useful spin-squeezed states[1-10] have been produced in large ensembles. These states have Gaussian spin distributions and therefore can largely be modeled as systems with a classical source of spin noise, where quantum mechanics enters only to set the amount of Gaussian noise. Non-Gaussian states with a negative Wigner function, however, are manifestly non-classical, since the Wigner function as a quasiprobability function must remain nonnegative in the classical realm. While prior to this work a negative Wigner function had not been attained for atomic ensembles, in the optical domain, a negativevalued Wigner function has very recently been measured for states with up to 110 microwave photons [18]. Another entanglement measure is the entanglement depth [19], i.e. the minimum number of atoms that are demonstrably, but possibly weakly, entangled with one another. This paramete...

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confidence: 99%

Entanglement with negative Wigner function of almost 3,000 atoms heralded by one photon

McConnell

Zhang

et al. 2015

Nature

212

218

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“…In spin squeezing, the uncertainty of one component of the (total) spin is reduced below the uncertainty limit at the expense of increased uncertainty in an orthogonal component 100 . Interestingly, it was shown theoretically that sufficiently strong spin squeezing implies entanglement in the spin bath 101 . As another example, although harder to achieve with current techniques, proposals exist for coherent exchange of a qubit state between the quantum dot electron spin and a collective degree of freedom of the nuclear spin bath 15 .…”

Section: Future Directions and Other Materialsmentioning

confidence: 99%

Nuclear spin effects in semiconductor quantum dots

et al. 2013

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“…We found that for values higher than N η = 10 4 we can achieve better results for the squeezing parameter improving further as the value of the cooperativity gets increased, a behavior we observe also in simulations with different N . Additionally, we compared the results of the optimized pulses with the adiabatic protocol of Sørensen and Mølmer [16] which achieves optimal squeezing for long time-scales and high cooperativities. In Fig.…”

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confidence: 99%

“…The second protocol, proposed by Sørensen and Mølmer, is based on adiabatic evolution to steer a system into maximally squeezed states squeezing the variance ∆ 2 J x under the constraint that J z is nonzero. [16].…”

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Noise-resistant optimal spin squeezing via quantum control

et al. 2016

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Entangled atomic states, such as spin squeezed states, represent a promising resource for a new generation of quantum sensors and atomic clocks. We demonstrate that optimal control techniques can be used to substantially enhance the degree of spin squeezing in strongly interacting many-body systems, even in the presence of noise and imperfections. Specifically, we present a protocol that is robust to noise which outperforms conventional methods. Potential experimental implementations are discussed.PACS numbers: 42.50. Dv, 02.30.Yy, 32.80.Qk Spin squeezed states are among the most interesting examples of entangled states. In quantum metrology they allow for measurements with an improved precision, ultimately limited only by the Heisenberg limit. Since the early theoretical proposals to realize them with non linear interactions [2,3], spin squeezed states have been implemented in several experiments. Specific examples include generation of spin squeezed states in cavity QED [4][5][6], in trapped ions through shared motional modes [7,8] or using a Bose-Einstein condensate [9,10].In this Letter we demonstrate that optimal control can be effectively employed to produce highly squeezed spin states in many-body quantum systems, drastically reducing the impact of relaxation and decoherence. Other approaches applied control techniques creating spin squeezing as a succession of unitary pulses of a constant Hamiltonian [11][12][13]. We employ the Chopped Random Basis (CRAB) technique [14,15] to optimally control the evolution of a collection of N two-level systems mutually coupled through a time-dependent non linear (i.e. quadratic) interaction. linear (i.e. quadratic) interaction. We calculate optimized evolutions occurring on time scales several orders of magnitude shorter than the corresponding adiabatic evolutions, with a speed-up increasing with the system size. Such a speed-up translates directly into an enhanced robustness of the squeezing in the presence of noise, as schematically depicted in Fig. 1. We illustrate this enhanced robustness by modelling two practical experimental implementations of squeezed state preparations: cavity QED and trapped ions [6,8].We will focus on two methods realizing spin squeezed states, both with advantages in different situations. The first is based on the so called one-axis twisting protocol, consisting in letting a collection of two-level systems evolve under the effect of a collective non linear interaction [3], described by a Hamiltonian of the formWhere ω is the precession frequency and χ is the strength of the nonlinear interaction and J is a collective spin operator (defined below). The relative simplicity of the one-axis twisting scheme has been at the basis of its ubiquitous presence in squeezing experiments; however such a scheme is known to be non optimal [3], the spherical nature of the angular momentum phase space limiting the maximal squeezing achievable. Such a bound is intrinsic for the one-axis twisting protocol with fixed χ. It nevertheless allows to achieve spi...

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Entanglement and Extreme Spin Squeezing

Cited by 426 publications

References 21 publications

Entanglement with negative Wigner function of almost 3,000 atoms heralded by one photon

Entanglement with negative Wigner function of almost 3,000 atoms heralded by one photon

Nuclear spin effects in semiconductor quantum dots

Noise-resistant optimal spin squeezing via quantum control

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