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:1707.04288 · Physical Review A

Shortcut to adiabaticity in a Stern-Gerlach apparatus

François Impens, David Guéry-Odelin

Published Oct 12, 2017• 16 citations
arXivHTMLPDF

Abstract

We show that the performances of a Stern-Gerlach apparatus can be improved by using a magnetic field profile for the atomic spin evolution designed with the shortcut-to-adiabaticity technique. Interestingly, it can be made more compact, for atomic beams propagating at a given velocity, and more resilient to a dispersion in velocity in comparison with the results obtained with a standard uniform rotation of the magnetic field. Our results are obtained using a reverse-engineering approach based on Lewis-Riesenfeld invariants. We discuss quantitatively the advantages offered by our configuration in terms of the resources involved and show that it drastically enhances the fidelity of the quantum state transfer achieved by the Stern-Gerlach device.

DOI
10.1103/physreva.96.043609

Related papers

Blurred path-spin entanglement in Stern-Gerlach apparatus: interplay between magnetic inhomogeneity and Larmor precession

Nirupam Dutta, Ansuman Dey

We argue that the non-adiabatic evolution of spin states in Stern-Gerlach apparatus can blur the manifestation of path spin entanglement. This fact introduces a contradiction to the usual perception of spin measurement even in a formally ideal situation. Through quantitative calculation, we have pointed out the specific reason behind the breakdown of adiabatic evolution to be the spatial inhomogeneity of applied magnetic field. The angle $θ$ between the $z$ component of magnetic moment of the particle and applied magnetic field is also a determining factor for the category of evolution of spin states. Adiabaticity always can be restored by choosing a sufficiently small value of $θ$. Considering azimuthal inhomogeneity, we have examined the nature of path spin entanglement in the context of Stern-Gerlach experiment.

arXiv:1410.4396•Oct 16, 2014•1 citation

Design of shortcuts to adiabaticity for Bose–Einstein condensate dynamics in soliton Josephson junctions

Jingru Wu, Chengyu Han, Qian Kong

Abstract This article primarily establishes a two-soliton system and employs the Lewis–Riesenfeld invariant inverse control method to achieve shortcuts to adiabaticity (STA) technology. We study an atomic soliton Josephson junctions (SJJs) device and subsequently compare and analyze it with atomic bosonic Josephson junctions. Moreover, we use higher-order expressions of the auxiliary equations to optimize the results and weaken the detrimental effect of the sloshing amplitude. We find that in the adiabatic shortcut evolution of two systems with time-containing tunnelling rates, the SJJs system is more robust over a rather short time evolution. In comparison with linear ramping, the STA technique is easier to achieve with the precise modulation of the quantum state in the SJJs system.

Communications in Theoretical Physics•Jul 2, 2024•2 citations

A Quantum Description of the Stern–Gerlach Experiment

Håkan Wennerström, Per-Olof Westlund

A detailed analysis of the classic Stern–Gerlach experiment is presented. An analytical simple solution is presented for the quantum description of the translational and spin dynamics of a silver atom in a magnetic field with a gradient along a single z-direction. This description is then used to obtain an approximate quantum description of the more realistic case with a magnetic field gradient also in a second y-direction. An explicit relation is derived for how an initial off center deviation in the y-direction affects the final result observed at the detector. This shows that the “mouth shape” pattern at the detector observed in the original Stern–Gerlach experiment is a generic consequence of the gradient in the y-direction. This is followed by a discussion of the spin dynamics during the entry of the silver atom into the magnet. An analytical relation is derived for a simplified case of a field only along the z-direction. A central question for the conceptual understanding of the Stern–Gerlach experiment has been how an initially unpolarized spin ends up in a polarized state at the detector. It is argued that this can be understood with the use of the adiabatic approximation. When the atoms first experience the magnetic field outside the magnet, there is in general a change in the spin state, which transforms from a degenerate eigenstate in the absence of a field into one of two possible non-degenerate states in the field. If the direction of the field changes during the passage through the device, there is a corresponding adiabatic change of the spin state. It is shown that an application of the adiabatic approximation in this way is consistent with the previously derived exact relations.

Entropy•Apr 25, 2017•14 citations

Visualisation of quantum evolution in the Stern–Gerlach and Rabi experiments

Marcel Utz, Malcolm H. Levitt, Nathan Cooper +1 more

The Stern-Gerlach experiment is a seminal experiment in quantum physics, involving the interaction between a particle with spin and an applied magnetic field gradient. A recent article [Wennerström et al., Phys. Chem. Chem. Phys., 2012, 14, 1677-1684] claimed that a full understanding of the Stern-Gerlach experiment can only be attained if transverse spin relaxation is taken into account, generated by fluctuating magnetic fields originating in the magnetic materials which generate the field gradient. This interpretation is contrary to the standard quantum description of the Stern-Gerlach experiment, which requires no dissipative effects. We present simulations of conventional quantum dynamics in the Stern-Gerlach experiment, using extended Wigner functions to describe the propagation of the quantum state in space and time. No relaxation effects are required to reproduce the qualitative experimental behaviour. We also present simulations of quantum dynamics in the Rabi experiment, in which an applied radiofrequency field induces spin transitions in the particle wave.

Physical Chemistry Chemical Physics•Dec 19, 2014•23 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

Robust coupled-waveguide devices using shortcuts to adiabaticity

Shuo‐Yen Tseng

Shortcuts to adiabaticity, originally developed in the context of quantum control, are powerful tools for the design of high coupling efficiency, robust, and short coupled-waveguide devices. The counterdiabatic protocol cancels the unwanted coupling in system evolution by the addition of a counterdiabatic term. The invariant-based inverse-engineering approach designs system evolution using the decoupled eigenstates of the Lewis-Riesenfeld invariant. The single-shot shaped-pulse technique directly parameterizes the solution of the coupled-mode equation. Starting from the counterdiabatic protocol, we show that these seemingly very different shortcuts to adiabaticity techniques are equivalent in the framework of coupled-waveguide systems. When combined with perturbation treatment of the coupled-mode equation, robust coupled-waveguide devices against errors can be obtained.

Optics Letters•Nov 14, 2014•51 citations
We show that the performances of a Stern-Gerlach apparatus can be improved by using a magnetic field profile for the atomic spin evolution designed with the shortcut-to-adiabaticity technique. Interestingly, it can be made more compact, for atomic beams propagating at a given velocity, and more resilient to a dispersion in velocity in comparison with the results obtained with a standard uniform rotation of the magnetic field. Our results are obtained using a reverse-engineering approach based on Lewis-Riesenfeld invariants. We discuss quantitatively the advantages offered by our configuration in terms of the resources involved and show that it drastically enhances the fidelity of the quantum state transfer achieved by the Stern-Gerlach device.
We argue that the non-adiabatic evolution of spin states in Stern-Gerlach apparatus can blur the manifestation of path spin entanglement. This fact introduces a contradiction to the usual perception of spin measurement even in a formally ideal situation. Through quantitative calculation, we have pointed out the specific reason behind the breakdown of adiabatic evolution to be the spatial inhomogeneity of applied magnetic field. The angle θθθ between the zzz component of magnetic moment of the particle and applied magnetic field is also a determining factor for the category of evolution of spin states. Adiabaticity always can be restored by choosing a sufficiently small value of θθθ. Considering azimuthal inhomogeneity, we have examined the nature of path spin entanglement in the context of Stern-Gerlach experiment.
Abstract This article primarily establishes a two-soliton system and employs the Lewis–Riesenfeld invariant inverse control method to achieve shortcuts to adiabaticity (STA) technology. We study an atomic soliton Josephson junctions (SJJs) device and subsequently compare and analyze it with atomic bosonic Josephson junctions. Moreover, we use higher-order expressions of the auxiliary equations to optimize the results and weaken the detrimental effect of the sloshing amplitude. We find that in the adiabatic shortcut evolution of two systems with time-containing tunnelling rates, the SJJs system is more robust over a rather short time evolution. In comparison with linear ramping, the STA technique is easier to achieve with the precise modulation of the quantum state in the SJJs system.
A detailed analysis of the classic Stern–Gerlach experiment is presented. An analytical simple solution is presented for the quantum description of the translational and spin dynamics of a silver atom in a magnetic field with a gradient along a single z-direction. This description is then used to obtain an approximate quantum description of the more realistic case with a magnetic field gradient also in a second y-direction. An explicit relation is derived for how an initial off center deviation in the y-direction affects the final result observed at the detector. This shows that the “mouth shape” pattern at the detector observed in the original Stern–Gerlach experiment is a generic consequence of the gradient in the y-direction. This is followed by a discussion of the spin dynamics during the entry of the silver atom into the magnet. An analytical relation is derived for a simplified case of a field only along the z-direction. A central question for the conceptual understanding of the Stern–Gerlach experiment has been how an initially unpolarized spin ends up in a polarized state at the detector. It is argued that this can be understood with the use of the adiabatic approximation. When the atoms first experience the magnetic field outside the magnet, there is in general a change in the spin state, which transforms from a degenerate eigenstate in the absence of a field into one of two possible non-degenerate states in the field. If the direction of the field changes during the passage through the device, there is a corresponding adiabatic change of the spin state. It is shown that an application of the adiabatic approximation in this way is consistent with the previously derived exact relations.
The Stern-Gerlach experiment is a seminal experiment in quantum physics, involving the interaction between a particle with spin and an applied magnetic field gradient. A recent article [Wennerström et al., Phys. Chem. Chem. Phys., 2012, 14, 1677-1684] claimed that a full understanding of the Stern-Gerlach experiment can only be attained if transverse spin relaxation is taken into account, generated by fluctuating magnetic fields originating in the magnetic materials which generate the field gradient. This interpretation is contrary to the standard quantum description of the Stern-Gerlach experiment, which requires no dissipative effects. We present simulations of conventional quantum dynamics in the Stern-Gerlach experiment, using extended Wigner functions to describe the propagation of the quantum state in space and time. No relaxation effects are required to reproduce the qualitative experimental behaviour. We also present simulations of quantum dynamics in the Rabi experiment, in which an applied radiofrequency field induces spin transitions in the particle wave.
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.
Shortcuts to adiabaticity, originally developed in the context of quantum control, are powerful tools for the design of high coupling efficiency, robust, and short coupled-waveguide devices. The counterdiabatic protocol cancels the unwanted coupling in system evolution by the addition of a counterdiabatic term. The invariant-based inverse-engineering approach designs system evolution using the decoupled eigenstates of the Lewis-Riesenfeld invariant. The single-shot shaped-pulse technique directly parameterizes the solution of the coupled-mode equation. Starting from the counterdiabatic protocol, we show that these seemingly very different shortcuts to adiabaticity techniques are equivalent in the framework of coupled-waveguide systems. When combined with perturbation treatment of the coupled-mode equation, robust coupled-waveguide devices against errors can be obtained.