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Physical Review A

Phase uncertainty and loss of interference in a simple model for mesoscopic Aharonov-Bohm experiments

Harry J. Lipkin

Published Jul 1, 1990• 4 citations
Publisher

Abstract

Incoherence introduced in two-path experiments by interactions with scatterers in thermal equilibrium is examined with an energy-momentum approach previously used for the M\"ossbauer effect. Oscillations in intensity with variations in the magnetic flux are shown to be insensitive to random phase changes in the individual scattering amplitudes. Inelastic incoherent scattering may be suppressed when there are a large number of scatterers. A small loss of phase coherence negligible in cases of practical interest can occur even via elastic scattering, which does not perturb the environment. The temperature dependence of the loss of interference, analogous to the Debye-Waller factor, may be tested by experiment.

DOI
10.1103/physreva.42.49

Related papers

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Given that it is now possible to observe the interference of molecules with comparatively numerous internal degrees of freedom, we might wonder what role these extra degrees of freedom play in the traditional double‐slit experiment. Here we seek to understand the effect of these degrees of freedom in an Aharonov‐Bohm type experiment. We find, perhaps unsurprisingly that an ionised object can exhibit the Aharonov‐Bohm effect in a manner which is independent of its internal structure. Meanwhile, the Aharonov‐Bohm type effects involving objects with magnetic, or electric dipole moments (the Aharonov‐Casher and He‐McKellar‐Wilkens effects, respectively) depend explicitly upon the structure. When—due to some specified dynamics of the internal variables—an object’s dipole moment changes during the experiment, we find that the corresponding phase shift depends upon the time average and variance of the internal dynamics. Furthermore, given that the internal dynamics are, to an extent, dependent upon the centre of mass motion there is also a small, transient loss of coherence associated with each internal degree of freedom.

AIP conference proceedings•Jan 1, 2009•0 citations
Incoherence introduced in two-path experiments by interactions with scatterers in thermal equilibrium is examined with an energy-momentum approach previously used for the M"ossbauer effect. Oscillations in intensity with variations in the magnetic flux are shown to be insensitive to random phase changes in the individual scattering amplitudes. Inelastic incoherent scattering may be suppressed when there are a large number of scatterers. A small loss of phase coherence negligible in cases of practical interest can occur even via elastic scattering, which does not perturb the environment. The temperature dependence of the loss of interference, analogous to the Debye-Waller factor, may be tested by experiment.
We study a simple model of dephasing of Aharonov-Bohm oscillations in the transmission of an electron across a mesoscopic ring. A magnetic impurity in one of the arms of the ring couples to the electron spin via an exchange interaction. This interaction leads to spin flip scattering and induces dephasing via entanglement. This is akin to the models evoked earlier to explain destruction of interference due to which-path information in double-slit experiments. Total transmission is found to be symmetric under flux reversal but not the spin polarization.
This work studies the interference of electrons in the presence of a line of magnetic flux surrounded by a normal-conducting mesoscopic cylinder at low temperature. It is found that, while there is a supplementary phase contribution from each electron of the mesoscopic cylinder, the sum of these individual supplementary phases is equal to zero, so that the presence of a normal-conducting mesoscopic ring at low temperature does not change the Aharonov-Bohm interference pattern of the incident electron. It is shown that it is not possible to ascertain by experimental observation that the shielding electrons have responded to the field of an incident electron, and at the same time to preserve the interference pattern of the incident electron. It is also shown that the measuring of the transient magnetic field in the region between the two paths of an electron interference experiment with an accuracy at least equal to the magnetic field of the incident electron generates a phase uncertainty which destroys the interference pattern.
We present a detailed analysis of the Aharonov-Bohm interference oscillations manifested through transmission of an electron in a mesoscopic ring with a magnetic impurity atom inserted in one of its arms. The electron interacts with the impurity through the exchange interaction leading to exchange spin-flip scattering. Transmission in the spin-flipped and spin-unflipped channels are explicitly calculated. We show that the spin-flipper acts as a dephasor in spite of absence of any inelastic scattering. The spin-conductance (related to spin-polarized transmission coefficient) is asymmetric in the flux reversal as opposed to the two probe conductance which is symmetric under flux reversal.
This note has no new results and is therefore not intended to be submitted to a "research" journal in the foreseeable future, but to be available to the numerous individuals who are interested in this issue. Several of those have approached the author for his opinion, which is summarized here in a hopefully pedagogical manner, for convenience. It is demonstrated, using essentially only energy conservation and elementary quantum mechanics, that true decoherence by a normal environment approaching the zero-temperature limit is impossible for a test particle which can not give or lose energy. Prime examples are: Bragg scattering, the Mössbauer effect and related phenomena at zero temperature, as well as quantum corrections for the transport of conduction electrons in solids. The last example is valid within the scattering formulation for the transport. Similar statements apply also to interference properties in equilibrium.
We investigate the influence that classical dynamics has on interference patterns in coherence experiments. We calculate the time-integrated probability current through an absorbing screen and the conductance through a doubly connected ballistic cavity, both in an Aharonov-Bohm geometry with forward scattering only. We show how interference fringes in the probability current generically disappear in the case of a chaotic system with small openings, and how they may persist in the case of an integrable cavity. Simultaneously, the typical, sample dependent amplitude of the flux-sensitive g(phi) part of the conductance survives in all cases, and becomes universal in the case of a chaotic cavity. In the presence of dephasing by fluctuations of the electric potential in one arm of the Aharonov-Bohm loop, we find an exponential damping of the flux-dependent part of the conductance, g(phi) proportional exp[-tauL/tauphi, in term of the traversal time tauL through the arm and the dephasing time tauphi. This extends previous works on dephasing in ballistic systems to the case of many conducting channels.
Given that it is now possible to observe the interference of molecules with comparatively numerous internal degrees of freedom, we might wonder what role these extra degrees of freedom play in the traditional double‐slit experiment. Here we seek to understand the effect of these degrees of freedom in an Aharonov‐Bohm type experiment. We find, perhaps unsurprisingly that an ionised object can exhibit the Aharonov‐Bohm effect in a manner which is independent of its internal structure. Meanwhile, the Aharonov‐Bohm type effects involving objects with magnetic, or electric dipole moments (the Aharonov‐Casher and He‐McKellar‐Wilkens effects, respectively) depend explicitly upon the structure. When—due to some specified dynamics of the internal variables—an object’s dipole moment changes during the experiment, we find that the corresponding phase shift depends upon the time average and variance of the internal dynamics. Furthermore, given that the internal dynamics are, to an extent, dependent upon the centre of mass motion there is also a small, transient loss of coherence associated with each internal degree of freedom.