Entangled mechanical oscillators

Jost, John D.; Home, Jonathan; Amini, Jason M.; Hanneke, David; Ozeri, Roee; Langer, C.; Bollinger, John J.; Leibfried, D.; Wineland, David J.

doi:10.1038/nature08006

Cited by 161 publications

(188 citation statements)

References 26 publications

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“…Moreover, rather than considering cases where quantum interference terms (the infamous "Schrödinger cat problem" [8,13,39]) vanish owing to decoherence processes [40], experimentalists have become able to control these very interferences [41], which are essential to describe the physics of quantum superpositions of macroscopic states and to explore the new possibilities offered by quantum information [22,42]. Examples include left and right going currents in superconducting circuits [15,43,44,45], macroscopic atomic ensembles [41] and entangled mechanical oscillators [46].…”

Section: General Features Of Quantum Measurementsmentioning

confidence: 99%

“…(E.2), that is, 46) where the coefficient a, given by 47) lies between 1 2 and 1. We define the second registration time τ reg as the delay taken by the average magnetization µ(t) to go from the paramagnetic value µ = 0 to the value m F − 1 2 m B close to m F .…”

Section: The Registration Process For a Second-order Transitionmentioning

confidence: 99%

“…The differences ∆ ± defined by (4.15) satisfy 46 You have to keep your balance 21) and give rise to derivatives with respect to m according to…”

Section: Large N Expansionmentioning

confidence: 99%

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Understanding quantum measurement from the solution of dynamical models

Allahverdyan¹,

Balian²,

2013

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The quantum measurement problem, to wit, understanding why a unique outcome is obtained in each individual experiment, is currently tackled by solving models. After an introduction we review the many dynamical models proposed over the years for elucidating quantum measurements. The approaches range from standard quantum theory, relying for instance on quantum statistical mechanics or on decoherence, to quantum-classical methods, to consistent histories and to modifications of the theory. Next, a flexible and rather realistic quantum model is introduced, describing the measurement of the z-component of a spin through interaction with a magnetic memory simulated by a Curie-Weiss magnet, including N 1 spins weakly coupled to a phonon bath. Initially prepared in a metastable paramagnetic state, it may transit to its up or down ferromagnetic state, triggered by its coupling with the tested spin, so that its magnetization acts as a pointer. A detailed solution of the dynamical equations is worked out, exhibiting several time scales. Conditions on the parameters of the model are found, which ensure that the process satisfies all the features of ideal measurements. Various imperfections of the measurement are discussed, as well as attempts of incompatible measurements. The first steps consist in the solution of the Hamiltonian dynamics for the spin-apparatus density matrixD(t). Its off-diagonal blocks in a basis selected by the spin-pointer coupling, rapidly decay owing to the many degrees of freedom of the pointer. Recurrences are ruled out either by some randomness of that coupling, or by the interaction with the bath. On a longer time scale, the trend towards equilibrium of the magnet produces a final stateD(t f ) that involves correlations between the system and the indications of the pointer, thus ensuring registration. AlthoughD(t f ) has the form expected for ideal measurements, it only describes a large set of runs. Individual runs are approached by analyzing the final states associated with all possible subensembles of runs, within a specified version of the statistical interpretation. There the difficulty lies in a quantum ambiguity: There exist many incompatible decompositions of the density matrixD(t f ) into a sum of sub-matrices, so that one cannot infer from its sole determination the states that would describe small subsets of runs. This difficulty is overcome by dynamics due to suitable interactions within the apparatus, which produce a special combination of relaxation and decoherence associated with the broken invariance of the pointer. Any subset of runs thus reaches over a brief delay a stable state which satisfies the same hierarchic property as in classical probability theory; the reduction of the state for each individual run follows. Standard quantum statistical mechanics alone appears sufficient to explain the occurrence of a unique answer in each run and the emergence of classicality in a measurement process. Finally, pedagogical exercises are proposed and lessons for future works on m...

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Section: General Features Of Quantum Measurementsmentioning

confidence: 99%

Section: The Registration Process For a Second-order Transitionmentioning

confidence: 99%

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Understanding quantum measurement from the solution of dynamical models

Allahverdyan¹,

Balian²,

2013

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“…In particular, stationary entanglement has been predicted between the cavity mode and a vibrating mirror [5][6][7][8][9], between an atomic ensemble or a Bose-Einstein condensate located inside an optical cavity and the vibrating mirror of the cavity [10][11][12][13], between two vibrating mirrors of a ring cavity [14], between two dielectric membranes suspended inside a cavity [15], and between a membrane and a trapped atom both located inside a cavity [16][17][18]. Further studies have addressed interesting problems of entangling mechanical oscillators [19], entangling optical and microwave cavity modes [20], and the creation of a photon by a vibrating mirror [21]. In this connection, we should mention the most recent work on the generation of entanglement in pulsed cavity optomechanics [22], and the work on the creation of entanglement between two oscillating mirrors through the coupling of the mirrors to an atomic system [23].…”

Section: Introductionmentioning

confidence: 99%

First-order coherence versus entanglement in a nanomechanical cavity

Sun

Ficek

2012

Phys. Rev. A

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The coherence and correlation properties of effective bosonic modes of a nano-mechanical cavity composed of an oscillating mirror and containing an optical lattice of regularly trapped atoms are studied. The system is modelled as a three-mode system, two orthogonal polariton modes representing the coupled optical lattice and the cavity mode, and one mechanical mode representing the oscillating mirror. We examine separately the cases of two-mode and three-mode interactions which are distinguished by a suitable tuning of the mechanical mode to the polariton mode frequencies. In the two-mode case, we find that the occurrence of entanglement in the system is highly sensitive to the presence of the first-order coherence between the modes. In particular, the creation of the first-order coherence among the polariton and mechanical modes is achieved at the expense of entanglement between them. In the three-mode case, we show that no entanglement is created between the independent polariton modes if both modes are coupled to the mechanical mode by the parametric interaction. There is no entanglement between the polaritons even if the oscillating mirror is damped by a squeezed vacuum field. The interaction creates the first-order coherence between the polaritons and the degree of coherence can, in principle, be as large as unity. This demonstrates that the oscillating mirror can establish the first-order coherence between two independent thermal modes. A further analysis shows that two independent thermal modes can be made entangled in the system only when one of the modes is coupled to the intermediate mode by a parametric interaction and the other is coupled by a linear-mixing interaction.

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“…Therefore, for lengthy algorithms, a method for recooling the ions is needed. This can be accomplished by combining the qubit ions with "refrigerant" ions that are cooled without disturbing the qubit states, but "sympathetically" cool the qubits through Coulomb coupling [7,8,[10][11][12][13][14][15]. Demonstrations of this technique in information processing have so far used sideband cooling [10][11][12][13][14].…”

mentioning

confidence: 99%

Sympathetic Electromagnetically-Induced-Transparency Laser Cooling of Motional Modes in an Ion Chain

et al. 2013

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We use electromagnetically induced transparency (EIT) laser cooling to cool motional modes of a linear ion chain. As a demonstration, we apply EIT cooling on 24 Mg + ions to cool the axial modes of a 9 Be + -24 Mg + ion pair and a 9 Be + -24 Mg + -24 Mg + -9 Be + ion chain, thereby sympathetically cooling the 9 Be + ions. Compared to previous implementations of conventional Raman sideband cooling, we achieve approximately an order-of-magnitude reduction in the duration required to cool the modes to near the ground state and significant reduction in required laser intensity.One proposal for building a quantum information processor is to use trapped, laser-cooled ions [1][2][3], where internal states of the ions serve as individual qubits that are manipulated by laser beams and/or microwave radiation. The Coulomb coupling between ions establishes normal modes of motion; transitions involving both the qubit states and motional modes enable entangling gate operations between multiple qubits. For high-fidelity deterministic entangling gates, we require that the thermal or uncontrolled components of the relevant modes be in the Lamb-Dicke regime [2], where the amplitude of the ions' uncontrolled motion is much less than the effective wavelength of the coupling radiation [4]. For most experiments this means that the motion must be cooled to near the quantum-mechanical ground state, which has typically been achieved with sideband laser cooling [2,5,6]. Scaling can potentially be achieved by storing ions in multi-zone arrays where information is moved in the processor by physically transporting the ions [7,8] or teleporting [9].Ion motion can be excited by ambient noisy electric fields and/or during ion transport [7]. Therefore, for lengthy algorithms, a method for recooling the ions is needed. This can be accomplished by combining the qubit ions with "refrigerant" ions that are cooled without disturbing the qubit states, but "sympathetically" cool the qubits through Coulomb coupling [7,8,[10][11][12][13][14][15]. Demonstrations of this technique in information processing have so far used sideband cooling [10][11][12][13][14]. While effective, sideband cooling can typically cool only one mode at a time, due to the differences in mode frequencies and narrowness of the sideband transitions. Furthermore, in the case of stimulated-Raman transition sideband cooling [6], the laser-beam intensities and detuning must be sufficiently large to avoid heating from spontaneous emission. Importantly, in experiments performed in this scalable configuration, the time required for re-cooling has been the limiting factor [12,16] and leads to errors due to qubit dephasing [17]. A technique that can mitigate these problems is EIT laser cooling, described theoretically in [18,19] and demonstrated on a single ion in [20][21][22]. For EIT cooling, required laser intensities are relatively small and the cooling bandwidth is large enough that multiple modes can be cooled simultaneously. To demonstrate these features, we investigate EIT cooling o...

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Entangled mechanical oscillators

Cited by 161 publications

References 26 publications

Understanding quantum measurement from the solution of dynamical models

Understanding quantum measurement from the solution of dynamical models

First-order coherence versus entanglement in a nanomechanical cavity

Sympathetic Electromagnetically-Induced-Transparency Laser Cooling of Motional Modes in an Ion Chain

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