A “Schrödinger Cat” Superposition State of an Atom

Monroe, Christopher; Meekhof, D. M.; King, B. E.; Wineland, David J.

doi:10.1126/science.272.5265.1131

Cited by 1,297 publications

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“…With laser cooling and a series of laser pulses to entangle the electronic and motional states they produced (displaced) even and odd coherent states [31,33].…”

Section: Discussionmentioning

confidence: 99%

Displaced and squeezed number states

1997

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After beginning with a short historical review of the concept of displaced (coherent) and squeezed states, we discuss previous (often forgotten) work on displaced and squeezed number states. Next, we obtain the most general displaced and squeezed number states. We do this in both the functional and operator (Fock) formalisms, thereby demonstrating the necessary equivalence. We then obtain the time-dependent expectation values, uncertainties, wave-functions, and probability densities. In conclusion, there is a discussion on the possibility of experimentally observing these states.

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“…With laser cooling and a series of laser pulses to entangle the electronic and motional states they produced (displaced) even and odd coherent states [31,33].…”

Section: Discussionmentioning

confidence: 99%

Displaced and squeezed number states

1997

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“…Here M = ρ 0 L 2 and ω k = (T 0 /ρ 0 ) 1 2 |k|. The coefficients F kk and K kk will be discussed below.…”

Section: Fig 1 (Color Online)mentioning

confidence: 99%

“…These phenomena have already been realized in many-particle contexts such as trapped ultracold atoms, 1 superconductors, 2 and photonic systems. 3 A current challenge is to observe these effects for collective degrees of freedom in a macroscopic context in, e.g., mechanical resonators.…”

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confidence: 99%

Generating macroscopic superposition states in nanomechanical graphene resonators

2012

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A theoretical study of the quantum dynamics of a symmetric nanomechanical graphene resonator with degenerate flexural modes is presented. Applying voltage pulses to two back gates, flexural vibrations of the membrane can be selectively actuated and manipulated. For graphene, nonlinear response becomes important for amplitudes comparable to the magnitude of zero-point fluctuations. We show, using analytical and numerical methods, that this allows for creation of catlike superpositions of coherent states as well as superpositions of coherent catlike nonproduct states. DOI: 10.1103/PhysRevB.85.205415 PACS number(s): 85.85.+j, 42.50.Dv, 73.50.Fq Coherent superposition of states are characteristic traits of quantum mechanics. These phenomena have already been realized in many-particle contexts such as trapped ultracold atoms, 1 superconductors, 2 and photonic systems. 3 A current challenge is to observe these effects for collective degrees of freedom in a macroscopic context in, e.g., mechanical resonators. 4 Recent advances in cooling mechanical resonators and sensitive displacement detection have allowed reaching the motional ground state and observing zero point fluctuations of center of mass. 5,6 Active manipulation and characterization of the quantum state of these systems, as already achieved with photons, 7 seem to be within reach. For a mechanical system, a desirable state to generate is a "cat" state. This is a coherent superposition of two minimum uncertainty wave packets separated by more than their individual quantum fluctuations.For the harmonic oscillator, a minimum uncertainty wave packet is a coherent state |α = exp[αa † − α * a]|0 generated by displacing the oscillator ground state. 8 As shown by Yurke and Stoler, 9 for a nonlinear oscillator H =hω 0n +h n 2 , an initial coherent state |α will after a time t = π/(2 ) evolve into the cat state (1/ √ 2)[e −iπ/4 |α + e iπ/4 |−α ] with the maximum spatial separation = 2|α|.Nanoelectromechanical resonators are typically intrinsically nonlinear. 10 Recent theoretical studies of their quantum dynamics show that it differs from the classical motion 11,12 and the nonlinearity can be exploited in the detection of the quantum signatures. The amplitudes needed to observe nonlinear effects are often orders of magnitude larger than the quantum zero-point fluctuations x 0 = √h /mω 0 . A cat state obtained due to this nonlinearity would have a separation 1. As the decoherence rate scales as 2 (see Refs. 13 and 14), this has, until now, been unfeasible. Instead, coupling to auxiliary quantum systems has been proposed to engineer the nonlinearity. 15,16 We show how, in the limit k B T hω 0 , the intrinsic nonlinearity of a graphene membrane resonator can be used to prepare cat states by applying voltage pulses to local backgates. The reason for using graphene is the ultralow mass of the graphene sheet, which leads to a large x 0 , and an onset of nonlinear response at small amplitudes. 17,18 This implies that cat states with moderate can be constructed without the...

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“…In particular, cold-atom schemes with BECs is one of the strongest candidates for a prototype of a scalable quantum information processor and is naturally fit for CV SCS schemes [30,31].…”

Section: Implementation For Entangled Scssmentioning

confidence: 99%

Generating non-classical states from spin coherent states via interaction with ancillary spins

Dooley

Joo

Proctor

et al. 2015

Optics Communications

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The generation of non-classical states of large quantum systems has attracted much interest from a foundational perspective, but also because of the significant potential of such states in emerging quantum technologies. In this paper we consider the possibility of generating non-classical states of a system of spins by interaction with an ancillary system, starting from an easily prepared initial state . We extend previous results for an ancillary system comprising a single spin to bigger ancillary systems and the interaction strength is enhanced by a factor of the number of ancillary spins. Depending on initial conditions, we find -by a combination of approximation and numerics -that the system of spins can evolve to spin cat states, spin squeezed states or to multiple cat states. * We also discuss some candidate systems for implementation of the Hamiltonian necessary to generate these non-classical states.

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A “Schrödinger Cat” Superposition State of an Atom

Cited by 1,297 publications

References 47 publications

Displaced and squeezed number states

Displaced and squeezed number states

Generating macroscopic superposition states in nanomechanical graphene resonators

Generating non-classical states from spin coherent states via interaction with ancillary spins

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