Continuous Weak Measurement and Nonlinear Dynamics in a Cold Spin Ensemble

Smith, Greg; Chaudhury, Souma; Silberfarb, Andrew; Deutsch, Ivan; Jessen, Poul

doi:10.1103/physrevlett.93.163602

Cited by 111 publications

(133 citation statements)

References 19 publications

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“…Weak measurement provides insight into a number of fundamental quantum effects, including the role of the uncertainty principle in the double-slit experiment [18], the Legget-Garg inequality [19], the quantum box problem [20], and Hardy's paradox [21]. It has also been used to amplify small experimental effects [22] and as feedback for control of a quantum system [23]. Weak measurements have been demonstrated in both classical [24] and non-classical systems [25].…”

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confidence: 99%

Procedure for Direct Measurement of General Quantum States Using Weak Measurement

2012

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Recent work [J.S. Lundeen et al. Nature, 474, 188 (2011)] directly measured the wavefunction by weakly measuring a variable followed by a normal (i.e. 'strong') measurement of the complementary variable. We generalize this method to mixed states by considering the weak measurement of various products of these observables, thereby providing the density matrix an operational definition in terms of a procedure for its direct measurement. The method only requires measurements in two bases and can be performed 'in situ', determining the quantum state without destroying it.PACS numbers: 03.65. Ta, 03.65.Wj, 42.50.Dv, The wavefunction Ψ is at the heart of quantum mechanics, yet its nature has been debated since its inception. It is typically relegated to being a calculational device for predicting measurement outcomes. Recently, Lundeen et al. proposed a simple and general operational definition of the wavefunction based on a method for its direct measurement: "it is the average result of a weak measurement of a variable followed by a strong measurement of the complementary variable [1,2]." By 'direct' it is meant that a value proportional to the wavefunction appears straight on the measurement apparatus itself without further complicated calculations or fitting. The 'wavefunction' referred to here is a special case of a general quantum state, known as a 'pure state.' The general case is represented by the density operator ρ, which can describe both pure and 'mixed' states. The latter incorporates both the effects of classical randomness (e.g., noise) and entanglement with other systems (e.g., decoherence). The density operator plays an important role in quantum statistics, quantum information, and the study of decoherence. Because of its generality and because it follows naturally from classical concepts of probability and measures, some consider ρ, rather than Ψ, to be the fundamental quantum state description. In this letter, we propose two methods to directly measure general quantum states, one of which directly gives the matrix elements of ρ.The standard method for experimentally determining the density operator is Quantum State Tomography [3]. In it, one makes a diverse set of measurements on an ensemble of identical systems and then determines the quantum state that is most compatible with the measurement results. An alternative is our direct measurement method, which may have advantages over tomography, such as simplicity, versatility, and directness. A quantitative comparison of measures such as the signal to noise ratio, resolution, and fidelity, has not been undertaken but some limitations of the direct method have been identified in [4]. As compared to tomography, which works with mixed states, the most significant limitation of the direct measurement of the wavefunction is that it has only been shown to work with pure states.Previous works have developed direct methods to measure quasi-probability distributions, such as the Wigner function [5], Husimi Q-function [6], and the GlauberSudarshan P-function [7]...

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Procedure for Direct Measurement of General Quantum States Using Weak Measurement

2012

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“…This quasiprobability has been inferred from weak-measurement experiments [50][51][52][53][54]. Weak measurements have been performed on cold atoms [58], which have been proposed as platforms for realizing scrambling and quantum chaos [15,16,59].…”

Section: Discussionmentioning

confidence: 99%

“…Interference and weak measurement have been performed with cold atoms [58], which have been proposed as platforms for realizing scrambling and quantum chaos [15,16,59]. Yet cold atoms are not necessary for measuringÃ ρ .…”

Section: Interference-based Measurement Ofã ρmentioning

confidence: 99%

Jarzynski-like equality for the out-of-time-ordered correlator

Halpern

2017

Phys. Rev. A

119

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The out-of-time-ordered correlator (OTOC) diagnoses quantum chaos and the scrambling of quantum information via the spread of entanglement. The OTOC encodes forward and reverse evolutions and has deep connections with the flow of time. So do fluctuation relations such as Jarzynski's equality, derived in nonequilibrium statistical mechanics. I unite these two powerful, seemingly disparate tools by deriving a Jarzynski-like equality for the OTOC. The equality's left-hand side equals the OTOC. The right-hand side suggests a protocol for measuring the OTOC indirectly. The protocol is platform-nonspecific and can be performed with weak measurement or with interference. Time evolution need not be reversed in any interference trial. The equality enables fluctuation relations to provide insights into holography, condensed matter, and quantum information and vice versa. DOI: 10.1103/PhysRevA.95.012120The out-of-time-ordered correlator (OTOC) F (t) diagnoses the scrambling of quantum information [1][2][3][4][5][6]: Entanglement can grow rapidly in a many-body quantum system, dispersing information throughout many degrees of freedom. F (t) quantifies the hopelessness of attempting to recover the information via local operations.Originally applied to superconductors [7], F (t) has undergone a revival recently. F (t) characterizes quantum chaos, holography, black holes, and condensed matter. The conjecture that black holes scramble quantum information at the greatest possible rate has been framed in terms of F (t) [6,8]. The slowest scramblers include disordered systems [9][10][11][12][13]. In the context of quantum channels, F (t) is related to the tripartite information [14]. Experiments have been proposed [15][16][17] and performed [18,19] to measure F (t) with cold atoms and ions, with cavity quantum electrodynamics, and with nuclear-magnetic-resonance quantum simulators.F (t) quantifies sensitivity to initial conditions, a signature of chaos. Consider a quantum system S governed by a Hamiltonian H . Suppose that S is initialized to a pure state |ψ and perturbed with a local unitary operator V . S then evolves forward in time under the unitary U = e −iH t for a duration t, is perturbed with a local unitary operator W, and evolves backward under U † . The state |ψ := U † WUV |ψ = W(t)V |ψ results. Suppose, instead, that S is perturbed with V not at the sequence's beginning, but at the end: |ψ evolves forward under U , is perturbed with W, evolves backward under U † , and is perturbed with V . The state |ψ := V U † WU |ψ = V W(t)|ψ results. The overlap between the two possible final states equals the correlator: push an ion-trap potential along some direction in space [26]. Let F := F (H f ) − F (H i ) denote the difference between the equilibrium free energies at the inverse temperature β: 1 F (H ) = − 1 β ln Z β, , wherein the partition function is Z β, := Tr(e −βH ) and = i or f . The free-energy difference has applications in chemistry, biology, and pharmacology [27]. One could measure F , in principle, by measuring th...

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“…1 describes a pure QND measurement. However, for f ≥ 1 atoms the G 2 term spoils the QND interaction even in the large-detuning limit [3,28]. To recover the ideal QND interaction, we use a two-polarization probing technique based on dynamical decoupling methods, described in detail in Ref.…”

Section: Optical Qnd Of Large-spin Atomsmentioning

confidence: 99%

Quantum metrology with cold atomic ensembles

Mitchell

Sewell

Napolitano

et al. 2013

EPJ Web of Conferences

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Abstract. Quantum metrology uses quantum features such as entanglement and squeezing to improve the sensitivity of quantum-limited measurements. Long established as a valuable technique in optical measurements such as gravitational-wave detection, quantum metrology is increasingly being applied to atomic instruments such as matter-wave interferometers, atomic clocks, and atomic magnetometers. Several of these new applications involve dual optical/atomic quantum systems, presenting both new challenges and new opportunities. Here we describe an optical magnetometry system that achieves both shot-noise-limited and projectionnoise-limited performance, allowing study of optical magnetometry in a fully-quantum regime [1]. By near-resonant Faraday rotation probing, we demonstrate measurement-based spin squeezing in a magnetically-sensitive atomic ensemble [2][3][4]. The versatility of this system allows us also to design metrologically-relevant optical nonlinearities, and to perform quantum-noise-limited measurements with interacting photons. As a first interaction-based measurement [5], we implement a non-linear metrology scheme proposed by Boixo et al. with the surprising feature of precision scaling better than the 1/N "Heisenberg limit" [6].

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Continuous Weak Measurement and Nonlinear Dynamics in a Cold Spin Ensemble

Cited by 111 publications

References 19 publications

Procedure for Direct Measurement of General Quantum States Using Weak Measurement

Procedure for Direct Measurement of General Quantum States Using Weak Measurement

Jarzynski-like equality for the out-of-time-ordered correlator

Quantum metrology with cold atomic ensembles

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