Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0310048 · Physical Review Letters

Fast Light, Slow Light, and Phase Singularities: A Connection to Generalized Weak Values

Daniel R. Solli, Colin F. McCormick, R. Y. Chiao, Sandu Popescu, J. Miguel Hickmann

Published Jan 29, 2004• 158 citations
arXivHTMLPDF

Abstract

We demonstrate that Aharonov-Albert-Vaidman weak values have a direct relationship with the response function of a system, and have a much wider range of applicability in both the classical and quantum domains than previously thought. Using this idea, we have built an optical system, based on a birefringent photonic crystal, with an infinite number of weak values. In this system, the propagation speed of a polarized light pulse displays both superluminal and slow light behavior with a sharp transition between the two regimes. We show that this system's response possesses two-dimensional, vortex-antivortex phase singularities. Important consequences for optical signal processing are discussed.

DOI
10.1103/physrevlett.92.043601

Related papers

Fast and slow light in an absorptionless, non-reflective system: a quantum weak measurement approach

Daniel R. Solli, Colin F. McCormick, Claus Ropers +4 more

We demonstrate that Aharonov-Albert-Vaidman weak values have a relationship with the response function of a system, in particular for a polarization based system with fast and slow light behavior, where Kramers-Kronig relations may not be valid.

Conference on Lasers and Electro-Optics•Jan 1, 2004•0 citations

Realization of a measurement of a ‘‘weak value’’

Nicholas W. M. Ritchie, J. G. Story, Randall G. Hulet

We present the first realization of a measurement of a ``weak value,'' a concept recently introduced by Aharonov, Albert, and Vaidman (AAV). Our experiment uses a birefringent crystal to separate the two linear-polarization components of a laser beam by a distance small compared to the laser-beam waist. This ``weak measurement'' is followed by a strong measurement which translates the centroid of the beam by a distance far larger than the birefringence-induced separation. In addition, we present data corresponding to orthogonal initial and final states, for which the weak value is not defined. This interference effect may have application in the amplification and detection of weak effects.

Physical Review Letters•Mar 4, 1991•594 citations

Collinear optical weak measurements with photonic crystals

Daniel R. Solli, Colin F. McCormick, Sandu Popescu +2 more

We present a theoretical and experimental study of a photonic crystal based optical system in terms of weak values that map polarization states onto longitudinal spatial position and show fast and slow light behavior.

arXiv:quant-ph/0309032•Sep 2, 2003•0 citations

On the connection between weak measurement in quantum physics and analytic phase-retrieval in classical wave optics

Nobuharu Nakajima

The physical interpretation of weak measurements has been the subject of much debate. It is known that anomalous phenomena and results that appear in weak measurements are essentially related to the phase of the quantum system being measured. Consideration of the phase is important to clarify its physical interpretation. In classical wave optics, there has long been studies on methods of measuring or retrieving the phase of a wave function. We here present that one of those methods, the analytic phase retrieval based on the properties of entire functions, has a close connection with weak measurements in quantum physics. We explain such a connection for two emblematic optical weak-measurements that have the same mathematical formalism as quantum systems: one is a system for weak measurements of polarized light displacement in a birefringent crystal, and the other is a system for the direct measurement of a wave function by weakly coupling it to a pointer. In those two systems, we show that the pre- and post-selection of polarized light provides a filtering effect similar to that utilized in the analytic phase retrieval.

arXiv:2312.15597•Dec 25, 2023•0 citations

Slow and Fast Light through Weak Measurements of Spectral Superoscillations

Thomas Zacharias, Liran Hareli, Alon Bahabad

Abstract Slow and fast light are light pulses moving at group velocities slower or faster than the speed of light in vacuum. Current methods to achieve slow and fast light are based on strong dispersion attainable in resonant systems. By defining slow and fast light based on the arrival of the expectation value of the pulse in time, an alternative route for achieving slow and fast light is experimentally demonstrated where no dispersion engineering is needed and thus can be applicable to any medium and system where light is propagating. The method is based on the phenomenon of superoscillations and entails a weak measurement of the arrival time of a light pulse. The findings can be useful for applications in telecommunication, interferometry, and laser radars.

Laser & Photonics Review•Aug 2, 2021•1 citation

Propagation of optical vector vortices of slow light in a coherently prepared tripod configuration

Dharma P. Permana, Mažena Mackoit Sinkevičienė, Julius Ruseckas +1 more

We investigate the propagation of optical vector vortices of slow light in a coherently prepared four-level tripod atomic system. The vector vortex consists of superposed pulse pairs with opposite circular polarizations and orbital angular momentum (OAM) charges $\pm l$, weakly interacting with an atomic medium initially prepared in a coherent superposition of two ground states. A third unoccupied state is coupled to a stronger control laser without OAM, creating a phase-dependent configuration. In the linear regime, the vortex OAM is mapped onto the medium, producing symmetrical azimuthally structured absorption patterns, with losses significantly reduced by the control field. For small detunings, complementary spatially dependent amplification and absorption occur for the two circular polarization components. This OAM-structured coherence induces a dynamical anisotropy, affecting both the intensity and polarization of the slow-light vortex. Polarization states evolve periodically between left-circular, linear, and right-circular polarizations during propagation. Once the beam reaches a stationary regime, the ring-shaped intensity transforms into a petal-like structure, and the final polarization states stabilize according to the initial superposition. The rate of polarization transitions is tunable via the control field strength, demonstrating flexible control over slow-light vector vortex dynamics.

quant-pharXiv:2603.23097•Chaos Solitons & Fractals•Mar 25, 2026•0 citations
We demonstrate that Aharonov-Albert-Vaidman weak values have a direct relationship with the response function of a system, and have a much wider range of applicability in both the classical and quantum domains than previously thought. Using this idea, we have built an optical system, based on a birefringent photonic crystal, with an infinite number of weak values. In this system, the propagation speed of a polarized light pulse displays both superluminal and slow light behavior with a sharp transition between the two regimes. We show that this system's response possesses two-dimensional, vortex-antivortex phase singularities. Important consequences for optical signal processing are discussed.
We present the first realization of a measurement of a ``weak value,'' a concept recently introduced by Aharonov, Albert, and Vaidman (AAV). Our experiment uses a birefringent crystal to separate the two linear-polarization components of a laser beam by a distance small compared to the laser-beam waist. This ``weak measurement'' is followed by a strong measurement which translates the centroid of the beam by a distance far larger than the birefringence-induced separation. In addition, we present data corresponding to orthogonal initial and final states, for which the weak value is not defined. This interference effect may have application in the amplification and detection of weak effects.
The physical interpretation of weak measurements has been the subject of much debate. It is known that anomalous phenomena and results that appear in weak measurements are essentially related to the phase of the quantum system being measured. Consideration of the phase is important to clarify its physical interpretation. In classical wave optics, there has long been studies on methods of measuring or retrieving the phase of a wave function. We here present that one of those methods, the analytic phase retrieval based on the properties of entire functions, has a close connection with weak measurements in quantum physics. We explain such a connection for two emblematic optical weak-measurements that have the same mathematical formalism as quantum systems: one is a system for weak measurements of polarized light displacement in a birefringent crystal, and the other is a system for the direct measurement of a wave function by weakly coupling it to a pointer. In those two systems, we show that the pre- and post-selection of polarized light provides a filtering effect similar to that utilized in the analytic phase retrieval.
Abstract Slow and fast light are light pulses moving at group velocities slower or faster than the speed of light in vacuum. Current methods to achieve slow and fast light are based on strong dispersion attainable in resonant systems. By defining slow and fast light based on the arrival of the expectation value of the pulse in time, an alternative route for achieving slow and fast light is experimentally demonstrated where no dispersion engineering is needed and thus can be applicable to any medium and system where light is propagating. The method is based on the phenomenon of superoscillations and entails a weak measurement of the arrival time of a light pulse. The findings can be useful for applications in telecommunication, interferometry, and laser radars.
We investigate the propagation of optical vector vortices of slow light in a coherently prepared four-level tripod atomic system. The vector vortex consists of superposed pulse pairs with opposite circular polarizations and orbital angular momentum (OAM) charges ±l\pm l±l, weakly interacting with an atomic medium initially prepared in a coherent superposition of two ground states. A third unoccupied state is coupled to a stronger control laser without OAM, creating a phase-dependent configuration. In the linear regime, the vortex OAM is mapped onto the medium, producing symmetrical azimuthally structured absorption patterns, with losses significantly reduced by the control field. For small detunings, complementary spatially dependent amplification and absorption occur for the two circular polarization components. This OAM-structured coherence induces a dynamical anisotropy, affecting both the intensity and polarization of the slow-light vortex. Polarization states evolve periodically between left-circular, linear, and right-circular polarizations during propagation. Once the beam reaches a stationary regime, the ring-shaped intensity transforms into a petal-like structure, and the final polarization states stabilize according to the initial superposition. The rate of polarization transitions is tunable via the control field strength, demonstrating flexible control over slow-light vector vortex dynamics.