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

Physical Review A

Spin coherence and Humpty-Dumpty. III. The effects of observation

Marlan O. Scully, Berthold‐Georg Englert, Julian Schwinger

Published Aug 1, 1989• 107 citations
Publisher

Abstract

In recent work a Stern-Gerlach interferometer (SGI) was considered in which a polarized beam of spin-(1/2 particles is split by a Stern-Gerlach apparatus into two partial beams, and then subsequent Stern-Gerlach deflecting magnets are used to reconstitute these two beams into one. In these studies it was shown that when such a coherent polarized beam passed through a SGI, some spin coherence is inevitably lost. In this regard, folk wisdom concerning irreversibility provides something of a guide to the present problem, since we all know that when Humpty-Dumpty had his great fall nobody could put him together again. In the present paper we consider the fate of our spin-(1/2 Humpty-Dumpty when a detector is present that is sensitive to the passage of particles along one trajectory, but not the other. It is not surprising that coherence is destroyed as soon as one is able to tell along which path the atom traveled. However, there seems to be no general agreement about the mechanism of coherence loss. Our conclusion is that the loss of coherence in measurements on quantum systems can always be traced to the dynamics of correlations between the measuring apparatus and the system being observed.

DOI
10.1103/physreva.40.1775

Related papers

Is spin coherence like Humpty-Dumpty. Pt. 2. General theory

Julian Schwinger, Marlan O. Scully, Berthold‐Georg Englert

A Stern-Gerlach interferometer combines Stern-Gerlach deflecting magnets to reconstitute initially split beams, in such a way that an arbitrary initial spin state is recovered. Technical and fundamental limitations on the realizability of the device are derived.

•Nov 1, 1988•1 citation

Irreversibility of a Stern-Gerlach experiment

Gourab Das, Rangeet Bhattacharyya

The Stern-Gerlach experiment (SGE) has been known for decades, but a complete theory that explains all facets of it remains enigmatic. In its classic realization, each spin state of an atom follows a unique path or trajectory in an SGE. The enigmatic part is the final output of SGE. Feynman envisaged the outcome to be an entangled state, a superposition of $|\text{spin}\phantom{\rule{4.pt}{0ex}}\text{state}\ensuremath{\rangle}\ensuremath{\bigotimes}|\text{corresponding}\phantom{\rule{4.pt}{0ex}}\text{path}\ensuremath{\rangle}$. Later works described the final state of SGE as a mixed state, a weighted average of states belonging to separate beams or trajectories. Notably, Schwinger, Englert, and Scully compared the difficulty of obtaining a coherent output (a pure state) to ``putting together Humpty Dumpty'' again. Yet recent experiments using Bose-Einstein condensates indicate the emerging beams are partly coherent, favoring Feynman's description. In this work, we revisit SGE using a recent version of the quantum master equation. We show that both outcomes are probable depending on the time of flight and the timescale of the environmental fluctuations. We predict the output is initially coherent and grows gradually into a mixed state. Moreover, we also estimate how the magnetic-field gradient helps broaden the beam waist. Moreover, our treatment implies that the wave function of an atom passing through a Stern-Gerlach device does not undergo an instantaneous collapse; rather, a gradual decay of coherences results in a mixed state, resulting in an irreversible process.

Physical Review A•Dec 11, 2024•1 citation

The Stern–Gerlach experiment and the effects of spin relaxation

Håkan Wennerström, Per-Olof Westlund

The classical Stern-Gerlach experiment is analyzed with an emphasis on the spin dynamics. The central question asked is whether there occurs a relaxation of the spin angular momentum during the time the particle passes through the Stern-Gerlach magnet. We examine in particular the transverse relaxation, involving angular momentum exchange between the spin of the particles and the spins of the magnet. A method is presented describing relaxation effects at an individual particle level. This leads to a stochastic equation of motion for the spins. This is coupled to a classical equation of motion for the particle translation. The experimental situation is then modeled through simulations of individual trajectories using two sets of parameter choices and three different sets of initial conditions. The two main conclusions are: (A) if the coupling between the magnet and the spin is solely described by the Zeeman interaction with the average magnetic field the simulations show a clear disagreement with the experimental observation of Stern and Gerlach. (B) If one, on the other hand, also allows for a T(2) relaxation time shorter than the passage time one can obtain a practically quantitative agreement with the experimental observations. These conclusions are at variance with the standard textbook explanation of the Stern-Gerlach experiment.

Physical Chemistry Chemical Physics•Dec 23, 2011•20 citations

Quantum correlations and measurements

Allan Roy Mackintosh, J Jensen

It is demonstrated that the collapse of the wavefunction in the quantum measurement process is reflected in the two-particle correlation function for the electron spin, which can in principle be studied by a triple Stern-Gerlach experiment. The change in momentum of a Stern-Gerlach magnet is itself sufficient to allow the determination of the electron spin, subject to the uncertainty principle, if the coherence of the two components of the spin is destroyed by the magnetic field. Similar considerations apply to the two-particle correlation function for the photon polarisation, and two-photon atomic cascades can be used in practice to investigate the measurement process and determine the extension of a photon wavepacket. The irreversibility of quantum mechanical measurements and its relation to the uncertainty principle is briefly considered.

European Journal of Physics•Oct 1, 1983•0 citations

Quantum coherence recovery through Stern–Gerlach erasure

Richard Barney, Jean-François S. Van Huele

Abstract Quantum erasure probes the dynamic nature of quantum coherence. It allows quantum systems to exhibit interference effects by recovering coherence that was previously lost through entanglement with another system. In this paper we examine the concept of a quantum eraser which creates and then erases path information through repeated use of the Stern–Gerlach effect. We explore the degree to which this eraser can recover quantum coherence. We find that the recovered coherence depends on the spin of the objects passing through the eraser and on the relative angle between the orientations of the eraser’s two magnets. We determine that full coherence can always be recovered for spin-1/2 objects independent of the value of the spin projection but cannot always be recovered for objects with larger spin values. We then discuss how the quantum coherence could be experimentally measured in this setup. Finally, we comment on the limitations of this Stern–Gerlach eraser and similar erasure schemes.

Physica Scripta•Jun 27, 2019•4 citations

Quantum Dynamical Simulation of a Transversal Stern–Gerlach Interferometer

Mikołaj M. Paraniak, Berthold‐Georg Englert

Originally conceived as a thought experiment, an apparatus consisting of two Stern–Gerlach apparatuses joined in an inverted manner touched on the fundamental question of the reversibility of evolution in quantum mechanics. Theoretical analysis showed that uniting the two partial beams requires an extreme level of experimental control, making the proposal in its original form unrealizable in practice. In this work, we revisit the above question in a numerical study concerning the possibility of partial-beam recombination in a spin-coherent manner. Using the Suzuki–Trotter numerical method of wave propagation and a configurable, approximation-free magnetic field, a simulation of a transversal Stern–Gerlach interferometer under ideal conditions is performed. The result confirms what has long been hinted at by theoretical analyses: the transversal Stern–Gerlach interferometer quantum dynamics is fundamentally irreversible even when perfect control of the associated magnetic fields and beams is assumed.

arXiv:2106.00205•Symmetry•Sep 8, 2021•9 citations
In recent work a Stern-Gerlach interferometer (SGI) was considered in which a polarized beam of spin-(1/2 particles is split by a Stern-Gerlach apparatus into two partial beams, and then subsequent Stern-Gerlach deflecting magnets are used to reconstitute these two beams into one. In these studies it was shown that when such a coherent polarized beam passed through a SGI, some spin coherence is inevitably lost. In this regard, folk wisdom concerning irreversibility provides something of a guide to the present problem, since we all know that when Humpty-Dumpty had his great fall nobody could put him together again. In the present paper we consider the fate of our spin-(1/2 Humpty-Dumpty when a detector is present that is sensitive to the passage of particles along one trajectory, but not the other. It is not surprising that coherence is destroyed as soon as one is able to tell along which path the atom traveled. However, there seems to be no general agreement about the mechanism of coherence loss. Our conclusion is that the loss of coherence in measurements on quantum systems can always be traced to the dynamics of correlations between the measuring apparatus and the system being observed.
The Stern-Gerlach experiment (SGE) has been known for decades, but a complete theory that explains all facets of it remains enigmatic. In its classic realization, each spin state of an atom follows a unique path or trajectory in an SGE. The enigmatic part is the final output of SGE. Feynman envisaged the outcome to be an entangled state, a superposition of $|\text{spin}\phantom{\rule{4.pt}{0ex}}\text{state}\ensuremath{\rangle}\ensuremath{\bigotimes}|\text{corresponding}\phantom{\rule{4.pt}{0ex}}\text{path}\ensuremath{\rangle}$. Later works described the final state of SGE as a mixed state, a weighted average of states belonging to separate beams or trajectories. Notably, Schwinger, Englert, and Scully compared the difficulty of obtaining a coherent output (a pure state) to ``putting together Humpty Dumpty'' again. Yet recent experiments using Bose-Einstein condensates indicate the emerging beams are partly coherent, favoring Feynman's description. In this work, we revisit SGE using a recent version of the quantum master equation. We show that both outcomes are probable depending on the time of flight and the timescale of the environmental fluctuations. We predict the output is initially coherent and grows gradually into a mixed state. Moreover, we also estimate how the magnetic-field gradient helps broaden the beam waist. Moreover, our treatment implies that the wave function of an atom passing through a Stern-Gerlach device does not undergo an instantaneous collapse; rather, a gradual decay of coherences results in a mixed state, resulting in an irreversible process.
The classical Stern-Gerlach experiment is analyzed with an emphasis on the spin dynamics. The central question asked is whether there occurs a relaxation of the spin angular momentum during the time the particle passes through the Stern-Gerlach magnet. We examine in particular the transverse relaxation, involving angular momentum exchange between the spin of the particles and the spins of the magnet. A method is presented describing relaxation effects at an individual particle level. This leads to a stochastic equation of motion for the spins. This is coupled to a classical equation of motion for the particle translation. The experimental situation is then modeled through simulations of individual trajectories using two sets of parameter choices and three different sets of initial conditions. The two main conclusions are: (A) if the coupling between the magnet and the spin is solely described by the Zeeman interaction with the average magnetic field the simulations show a clear disagreement with the experimental observation of Stern and Gerlach. (B) If one, on the other hand, also allows for a T(2) relaxation time shorter than the passage time one can obtain a practically quantitative agreement with the experimental observations. These conclusions are at variance with the standard textbook explanation of the Stern-Gerlach experiment.
It is demonstrated that the collapse of the wavefunction in the quantum measurement process is reflected in the two-particle correlation function for the electron spin, which can in principle be studied by a triple Stern-Gerlach experiment. The change in momentum of a Stern-Gerlach magnet is itself sufficient to allow the determination of the electron spin, subject to the uncertainty principle, if the coherence of the two components of the spin is destroyed by the magnetic field. Similar considerations apply to the two-particle correlation function for the photon polarisation, and two-photon atomic cascades can be used in practice to investigate the measurement process and determine the extension of a photon wavepacket. The irreversibility of quantum mechanical measurements and its relation to the uncertainty principle is briefly considered.
Abstract Quantum erasure probes the dynamic nature of quantum coherence. It allows quantum systems to exhibit interference effects by recovering coherence that was previously lost through entanglement with another system. In this paper we examine the concept of a quantum eraser which creates and then erases path information through repeated use of the Stern–Gerlach effect. We explore the degree to which this eraser can recover quantum coherence. We find that the recovered coherence depends on the spin of the objects passing through the eraser and on the relative angle between the orientations of the eraser’s two magnets. We determine that full coherence can always be recovered for spin-1/2 objects independent of the value of the spin projection but cannot always be recovered for objects with larger spin values. We then discuss how the quantum coherence could be experimentally measured in this setup. Finally, we comment on the limitations of this Stern–Gerlach eraser and similar erasure schemes.
Originally conceived as a thought experiment, an apparatus consisting of two Stern–Gerlach apparatuses joined in an inverted manner touched on the fundamental question of the reversibility of evolution in quantum mechanics. Theoretical analysis showed that uniting the two partial beams requires an extreme level of experimental control, making the proposal in its original form unrealizable in practice. In this work, we revisit the above question in a numerical study concerning the possibility of partial-beam recombination in a spin-coherent manner. Using the Suzuki–Trotter numerical method of wave propagation and a configurable, approximation-free magnetic field, a simulation of a transversal Stern–Gerlach interferometer under ideal conditions is performed. The result confirms what has long been hinted at by theoretical analyses: the transversal Stern–Gerlach interferometer quantum dynamics is fundamentally irreversible even when perfect control of the associated magnetic fields and beams is assumed.