Environment-induced decoherence I. The Stern-Gerlach measurement

Venugopalan, Anu; Kumar, Deepak; Ghosh, R.

doi:10.1016/0378-4371(95)00184-9

Cited by 29 publications

(37 citation statements)

References 24 publications

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“…For the coordinatecoordinate coupling model, the position basis is intuitively expected to emerge as the preferred basis. However, this is contrary to the conclusion of Venugopalan et al [10] in their analysis of the Stern-Gerlach measurement model where the spin components eventually correlate with distributions which are completely diagonal in the momentum basis and only approximately diagonal in the position basis [10]. In the literature, the preferred basis has been variously described as the one in which the final state density matrix becomes diagonal or that set of basis states which are characterized by maximum stability or a minimum increase in linear or statistical entropy, decided by a 'predictability sieve' [17].…”

Section: Introductioncontrasting

confidence: 90%

“…where s, s ′ = +1 (or ↑ ) or −1 (or ↓). Thus (2) represents four equations in the coordinate representation, each corresponding to one of the four elements in spin space (↑↑, ↑↓, ↓↑, ↓↓) of the reduced density matrix for the systemapparatus combine [10]. Here γ is the relaxation rate and…”

Section: Reduced Density Matrix For the System-apparatusmentioning

confidence: 99%

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Pointer states via decoherence in a quantum measurement

Venugopalan

1999

Phys. Rev. A

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We consider the interaction of a quantum system ͑spin-1 2 ) with a macroscopic quantum apparatus ͑harmonic oscillator͒ which in turn is coupled to a bath of harmonic oscillators. Exact solutions of the Markovian master equation show that the reduced density matrix of the system-apparatus combination decoheres to a statistical mixture where up and down spins eventually correlate with pointer states of the apparatus ͑harmonic oscillator͒, with associated probabilities in accordance with quantum principles. For the zero-temperature bath these pointer states turn out to be coherent states of the harmonic oscillator ͑apparatus͒ for arbitrary initial states of the apparatus. Further, we see that the decoherence time is inversely proportional to the square of the separation between the two coherent states with which the spins correlate. For a high-temperature bath, pointer states no longer remain coherent states but are Gaussian distributions ͑generalized coherent states͒. Spin up and down states of the system now correlate with nearly diagonal distributions in position of these generalized coherent states. The diagonalization in position increases with the temperature of the bath. The off-diagonal elements in spin space decohere over a time scale which goes inversely as the square of the separation between the peaks of the two position distributions that correlate with the spin states. Zurek's earlier approximate result for the decoherence time is consistent with our exact results. Our analysis brings out the importance of looking at a measurementlike scenario where definite correlations are established between the system and apparatus to determine the nature of the pointer basis of the apparatus. Further, our exact results demonstrate in an unambiguous way that the pointer states in this measurement model emerge independent of the initial state of the apparatus.

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Section: Introductioncontrasting

confidence: 90%

Section: Reduced Density Matrix For the System-apparatusmentioning

confidence: 99%

Pointer states via decoherence in a quantum measurement

Venugopalan

1999

Phys. Rev. A

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“…The time evolution under the influence of this Hamiltonian can be worked out explicitly. 24) The state of the particle, when it reaches the screen is given by 24) …”

Section: §3 Example With Gaussian Wave Packetsmentioning

confidence: 99%

Quantum Eraser Using a Modified Stern-Gerlach Setup

Qureshi

Rahman

2012

Progress of Theoretical Physics

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We propose a new setup to demonstrate quantum eraser, using spin-1/2 particles in a modified Stern-Gerlach setup, with a double slit. The which-way information can be erased simply by applying a transverse magnetic field with an additional magnet, resulting in the emergence of two complementary staggered interference patterns. Use of the classic SternGerlach setup, and the unweaving of the washed out interference without any coincident counting, is what makes this proposal novel.Subject Index: 061 §1. Complementarity and quantum eraser

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“…Of particular relevance here is the case of "ohmic coupling", which gives the correct limit of classical dissipation. For our analysis, we deal directly with the Markovian master equation for the reduced density matrix of the system in the position representation, where the environmental degrees of freedom have been traced out [18,19,20]:…”

Section: Theoretical Analysis a Coupling To The Environmentmentioning

confidence: 99%

Decoherence and Matter Wave Interferometry

Qureshi

Venugopalan

2008

Int. J. Mod. Phys. B

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A two-slit interference of a massive particle in the presence of environment induced decoherence is theoretically analyzed. The Markovian Master equation, derived from coupling the particle to a harmonic-oscillator heat bath, is used to obtain exact solutions which show the existence of an interference pattern. Interestingly, decoherence does not affect the pattern, but only leads to a reduction in the fringe visibility.

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Environment-induced decoherence I. The Stern-Gerlach measurement

Cited by 29 publications

References 24 publications

Pointer states via decoherence in a quantum measurement

Pointer states via decoherence in a quantum measurement

Quantum Eraser Using a Modified Stern-Gerlach Setup

Decoherence and Matter Wave Interferometry

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