Operational formulation of weak values without probe systems

Ogawa, Kensuke; Kobayashi, H.; Tomita, Akira

doi:10.1103/physreva.101.042117

Cited by 13 publications

(5 citation statements)

References 49 publications

(131 reference statements)

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“…In a similar way, the weak moment is expected to play an important role in other problems of this kind. In addition, the use of measurement methods other than the weak measurements with Gaussian probes-such as weak measurement using a qubit probe [48] and the method without a probe [49]-may find new implications for the weak moments.…”

Section: Discussionmentioning

confidence: 99%

Complex counterpart of variance in quantum measurements for pre- and post-selected systems

Ogawa,

Abe,

Kobayashi

et al. 2021

Preprint

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The variance of an observable for a preselected quantum system, which is always real and nonnegative, appears in the increase of the probe wave packet width in indirect measurement. We extend this framework to pre-and postselected systems, and formulate a complex-valued counterpart of the variance called "weak variance." In our formulation, the real and imaginary parts of the weak variance appear in the changes in the probe wave packet width in vertical-horizontal and diagonalantidiagonal directions on the quadrature phase plane, respectively. Using an optical system, we experimentally demonstrate these changes in a probe wave packet width caused by the real negative and pure imaginary weak variances. Furthermore, we describe that the weak variance can be expressed as the variance of the weak-valued probability distribution for pre-and post-selected systems. These operational and statistical interpretations support that our formulation of the weak variance is reasonable as a complex counterpart of the variance for pre-and post-selected systems.

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Section: Discussionmentioning

confidence: 99%

Complex counterpart of variance in quantum measurements for pre- and post-selected systems

Ogawa,

Abe,

Kobayashi

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

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“…It is straightforward to extend this scheme to an arbitrary number of operators. Note that it has also been shown that the imaginary part of a WV can be measured using a small phase shift without a probe ( 39 , 20 ). Therefore, using an approach similar to that shown here, it may be possible to apply it for an arbitrary magnitude of phase to find the sign of the imaginary parts of WVs (although this was not required for the current analysis).…”

Section: Methodsmentioning

confidence: 99%

“…In this method, the WV appears in the change of the postselection probability amplitude when a small attenuation is given between the pre- and postselections. Recently, this method has been theoretically generalized, for example, so as to be applicable to a quantum system in mixed states ( 20 ). However, the way to measure SWVs was not presented and the degree of attenuation was restricted to be weak.…”

Section: Measurement Of Swvsmentioning

confidence: 99%

Experimentally probing anomalous time evolution of a single photon

Okamoto

Cohen

2023

PNAS Nexus

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In quantum mechanics, a quantum system is irreversibly collapsed by a projective measurement. Hence, delicately probing the time evolution of a quantum system holds the key to understanding curious phenomena. Here we experimentally explore an anomalous time evolution, where, illustratively, a particle disappears from a box and emerges in a different box, with a certain moment in which it can be found in neither of them. In this experiment, we directly probe this curious time evolution of a single photon by measuring up to triple-operator sequential weak values using a novel probeless scheme. The naive interpretation provided by single-operator weak values seems to imply the “disappearance” and “re-appearance” of a photon as theoretically predicted. However, double- and triple-operator sequential weak values, representing temporal correlations between the aforementioned values, show that spatial information about the photon does not entirely vanish in the intermediate time. These results show that local values (in space and time) alone, such as single-operator weak values, cannot fully explain all types of quantum evolution in time - higher order correlations are necessary in general, shedding new light on time evolution in quantum mechanics. The probeless measurement technique proposed here for measuring multiple-operator weak values can be straightforwardly extended to study various other cases of curious quantum evolution in time.

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“…Comparison between experiment and theory revealed that the XTAS signal was reporting the nuclear motion over the duration of the relaxation process. It is important to consider that SFI experiments could potentially exhibit electronic relaxation dynamics without considerable nuclear motion, involving highly excited Rydberg or cationic states (38,39). To prove that the observed XTAS signal dynamics solely arose from nuclear (rather than electronic) relaxation, we performed experiments and computations for the dynamics after SFI of CD 4 .…”

Section: Relaxation Dynamics Of Ch 4 +mentioning

confidence: 99%

Femtosecond symmetry breaking and coherent relaxation of methane cations via x-ray spectroscopy

Ridente

Hait

Haugen

et al. 2023

Science

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Understanding the relaxation pathways of photoexcited molecules is essential to gain atomistic level insight into photochemistry. Herein, we performed a time-resolved study of ultrafast molecular symmetry breaking via geometric relaxation (Jahn-Teller distortion) on the methane cation. Attosecond transient absorption spectroscopy with soft X-rays at the carbon K-edge revealed that the distortion occurred within 10 ± 2 femtoseconds after few-femtosecond strong-field ionization of methane. The distortion activated coherent oscillations in the asymmetric scissoring vibrational mode of the symmetry broken cation, which were detected in the X-ray signal. These oscillations were damped within 58 ± 13 femtoseconds, as vibrational coherence was lost with the energy redistributing into lower-frequency vibrational modes. This study completely reconstructs the molecular relaxation dynamics of this prototypical example and opens new avenues for exploring complex systems.

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Operational formulation of weak values without probe systems

Cited by 13 publications

References 49 publications

Complex counterpart of variance in quantum measurements for pre- and post-selected systems

Complex counterpart of variance in quantum measurements for pre- and post-selected systems

Experimentally probing anomalous time evolution of a single photon

Femtosecond symmetry breaking and coherent relaxation of methane cations via x-ray spectroscopy

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