Geometric phase topology in weak measurement

Samlan, C. T.; Viswanathan, Nirmal K.

doi:10.1088/2040-8986/aa9294

Cited by 2 publications

(3 citation statements)

References 43 publications

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“…The central theme of the weak measurement revolves around optimal exploitation of a nonlinear relationship that exists between the quantity to be measured and quantity being sensed [10][11][12][13][14]. This is achieved by a near orthogonal projection of the probe/preselected state |ψ I ⟩ on post-selected state |ψ F ⟩ [8-12].…”

Section: Theory and Simulationmentioning

confidence: 99%

“…It should be kept in mind that, due to the limited time response of the available detectors in the optical regime of electromagnetic spectrum, we only measure the intensity or the energy of the field. The weak interaction is sensed through the shift in centroid of the intensity of the post selected state [8][9][10][11]. The phase of the output state is rarely looked upon.…”

Section: Weak Measurement Scheme In Interferometrymentioning

confidence: 99%

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Amplified sensing of optical phase difference through the phase of the resultant field

Athira¹,

Naik²

2021

J. Opt.

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A generalized scheme to enhance the sensitivity in the measurement of phase difference in an optical interference by measuring the phase of the resultant field is presented. In the proposed scheme, the weak measurement in scalar optical interferometry is achieved by directly accessing the phase of the output state, rather than looking at the centroid shift in the intensity. The spatial confinement or beam-like characteristics for the optical field, an essential criterion for centroid calculation, is not a requirement for the scheme. The ability to uniquely sense and distinguish contributions to the phase difference from individual optical fields; an aspect with potential to improve the measurement accuracy in optical gyroscopes and gravitational wave sensing, is also presented.

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Section: Theory and Simulationmentioning

confidence: 99%

Section: Weak Measurement Scheme In Interferometrymentioning

confidence: 99%

Amplified sensing of optical phase difference through the phase of the resultant field

Athira¹,

Naik²

2021

J. Opt.

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“…Ho and Imoto related the polar decomposition of modular values to geometric phases as well [62]. Geometric phases in weak measurements were also considered in the context of the spin Hall effect of light [63,64] and for sequential measurements [65]. The link between weak values and the Bargmann invariant [66] was noted on multiple occasions [58,59,61,67].…”

Section: Introductionmentioning

confidence: 99%

Geometrical interpretation of the argument of weak values of general observables in N-level quantum systems

Ferraz

Lambert²,

Caudano³

2022

Quantum Sci. Technol.

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Observations in quantum weak measurements are determined by complex numbers called weak values. We present a geometrical interpretation of the argument of weak values of general Hermitian observables in N-dimensional quantum systems in terms of geometric phases. We formulate an arbitrary weak value in function of three real vectors on the unit sphere in N 2 − 1 dimensions, S N 2 −2. These vectors are linked to the initial and final states, and to the weakly measured observable, respectively. We express pure states in the complex projective space of N − 1 dimensions, CP N−1, which has a non-trivial representation as a 2N − 2 dimensional submanifold of S N 2−2 (a generalization of the Bloch sphere for qudits). The argument of the weak value of a projector on a pure state of an N-level quantum system describes a geometric phase associated to the symplectic area of the geodesic triangle spanned by the vectors representing the pre-selected state, the projector and the post-selected state in CP N−1. We then proceed to show that the argument of the weak value of a general observable is equivalent to the argument of an effective Bargmann invariant. Hence, we extend the geometrical interpretation of projector weak values to weak values of general observables. In particular, we consider the generators of SU(N) given by the generalized Gell-Mann matrices. Finally, we study in detail the case of the argument of weak values of general observables in two-level systems and we illustrate weak measurements in larger dimensional systems by considering projectors on degenerate subspaces, as well as Hermitian quantum gates.

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Geometric phase topology in weak measurement

Cited by 2 publications

References 43 publications

Amplified sensing of optical phase difference through the phase of the resultant field

Amplified sensing of optical phase difference through the phase of the resultant field

Geometrical interpretation of the argument of weak values of general observables in N-level quantum systems

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