Introduction to Quantum Metrology

Nawrocki, Waldemar

doi:10.1007/978-3-319-15669-9

Cited by 9 publications

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“…They are also expected to exhibit the phenomenon of quantum evaporation, whereby an elementary excitation of a superfluid reaches its surface and causes the evaporation of a single atom. This phenomenon had so far been studied experimentally [17,18] and theoretically [19,20] in superfluid 4 He, and we consider it for the first time in the context of superfluid atomic gases.…”

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confidence: 99%

Quantized conductance through the quantum evaporation of bosonic atoms

2016

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We analyze theoretically the quantization of conductance occurring with cold bosonic atoms trapped in two reservoirs connected by a constriction with an attractive gate potential. We focus on temperatures slightly above the condensation threshold in the reservoirs. We show that a conductance step occurs, coinciding with the appearance of a condensate in the constriction. Conductance relies on a collective process involving the quantum condensation of an atom into an elementary excitation and the subsequent quantum evaporation of an atom, in contrast with ballistic fermion transport. The value of the bosonic conductance plateau is strongly enhanced compared to fermions and explicitly depends on temperature. We highlight the role of the repulsive interactions between the bosons in preventing them from collapsing into the constriction.PACS numbers: 05.60. Gg,05.30.Jp, In mesoscopic systems, where the motion of quantum particles occurs over distances of the order of their coherence length, transport phenomena exhibit quantum signatures [1]. The quantization of conductance [2] is a hallmark among these effects. It reflects the discrete nature of the transport channels inside a strongly constricted geometry, and it occurs if the spread in energies of the incident particle distribution is smaller than the energy separation of these channels. It was first observed in electronic transport through a quantum point contact [3] as a series of plateaux in the conductance when the distance between the gate electrodes was increased. In this fermionic case, the conductance quantum G K = e 2 /h involves fundamental constants only, which makes it relevant for metrology [4, chap. 7]. Unlike the quantum Hall effect [5], it occurs in the absence of a magnetic field and has been predicted to affect neutral Helium atoms [6].Conductance quantization has recently been observed in ultracold fermionic gases [7]. Atomic gases allow for a clean observation in a simple setup involving two reservoirs connected by a constriction within which an attractive gate potential E G < 0 is varied (see Fig. 1). Experiments on ultracold fermions aim at simulating electronic systems using neutral particles [7][8][9][10]. In the fermionic experiment of Ref. [7], conductance quantization has been observed at temperatures much lower than both the Fermi temperature T F and the confinement energy of the constriction, in analogy with the original results on electronic transport [3] where only particles near the Fermi surface take part in transport phenomena. This raises the question of whether conductance quantization also affects bosons. Previous observations in an optical setup [11,12] and predictions with cold matter waves [13] have focused on systems where all particles have the same incident energy, mimicking fermionic transport at the Fermi energy. To our knowledge, the specific role of bosonic statistics in quantized conductance situations has not yet been investigated. Cold atom setups allow for theTwo reservoirs (L, R) can exchange particles through a s...

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confidence: 99%

Quantized conductance through the quantum evaporation of bosonic atoms

2016

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“…From a practical point of view, quantum information science requires ever better control of microscopic systems and, hence, measurements which are as accurate as possible. More specifically, quantum metrology [4] aims at finding bounds on the achievable measurement precision and at identifying states which would be optimal for quantum measurements or other specific tasks. The optimal transmission of a Cartesian frame [5] or the efficient detection of inhomogeneous magnetic fields [6] are typical examples.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

“…The latter have been tabulated up to j = 50[31]. For example, the first pairs (t, j) for j 4 are given by (1, 1), (1, 3/2), (2, 2), (1, 5/2), (3, 3), (2, 7/2),(3,4).…”

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Optimal Detection of Rotations about Unknown Axes by Coherent and Anticoherent States

Martin

Weigert

Giraud

2020

Quantum

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Coherent and anticoherent states of spin systems up to spin j=2 are known to be optimal in order to detect rotations by a known angle but unknown rotation axis. These optimal quantum rotosensors are characterized by minimal fidelity, given by the overlap of a state before and after a rotation, averaged over all directions in space. We calculate a closed-form expression for the average fidelity in terms of anticoherent measures, valid for arbitrary values of the quantum number j. We identify optimal rotosensors (i) for arbitrary rotation angles in the case of spin quantum numbers up to j=7/2 and (ii) for small rotation angles in the case of spin quantum numbers up to j=5. The closed-form expression we derive allows us to explain the central role of anticoherence measures in the problem of optimal detection of rotation angles for arbitrary values of j.

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“…From a practical point of view, quantum information science requires ever better control of microscopic systems and, hence, measurements which are as accurate as possible. More specifically, quantum metrology [4] aims at finding bounds on the achievable measurement precision and at identifying states which would be optimal for quantum measurements. While the classical Cramér-Rao theorem [5,6] provides a lower bound on the variance of random estimators by means of the Fisher information, its quantummechanical counterpart provides bounds for quantum parameter estimation theory [7].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Optimal Detection of Rotations about Unknown Axes by Coherent and Anticoherent States

Martin,

Weigert,

Giraud

2019

Preprint

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Coherent and anticoherent states of spin systems up to spin j = 2 are known to be optimal in order to detect rotations by a known angle but unknown rotation axis. These optimal quantum rotosensors are characterized by minimal fidelity, given by the overlap of a state before and after a rotation, averaged over all directions in space. We calculate a closed-form expression for the average fidelity in terms of anticoherent measures, valid for arbitrary values of the quantum number j. We identify optimal rotosensors (i) for arbitrary rotation angles in the case of spin quantum numbers up to j = 7/2 and (ii) for small rotation angles in the case of spin quantum numbers up to j = 5. The closed-form expression we derive allows us explain the central role of anticoherence measures in the problem of optimal detection of rotation angles for arbitrary values of j.

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Introduction to Quantum Metrology

Cited by 9 publications

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Quantized conductance through the quantum evaporation of bosonic atoms

Quantized conductance through the quantum evaporation of bosonic atoms

Optimal Detection of Rotations about Unknown Axes by Coherent and Anticoherent States

Optimal Detection of Rotations about Unknown Axes by Coherent and Anticoherent States

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