Geometric Phases for Mixed States in Interferometry

Sjöqvist, Erik; Pati, Arun Kumar; Ekert, Artur; Anandan, J.; Ericsson, Marie; Oi, Daniel K. L.; Vedral, Vlatko

doi:10.1103/physrevlett.85.2845

Cited by 557 publications

(746 citation statements)

References 25 publications

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“…Therefore, the interference pattern given by Eq.7 takes the following form for a mixed input spin state [11],…”

Section: Theory Quantum Interferencementioning

confidence: 99%

“…As the phase shifter and the unitary operator 'U' are path specific, they are represented by two controlled operations, together given by [11],…”

Section: Theory Quantum Interferencementioning

confidence: 99%

“…The oscillation pattern of the probability resembles the well known optical interference pattern. According to Sjöqvist et al the shift of interference pattern is a function of the geometric phase acquired by the quantum system during the unitary evolutions, as well as the purity of the initial internal state (such as, polarization of a photon) of the quantum systems involved in the interferometric operation [11]. The geometric phase can be directly measured from the shift of the interference pattern.…”

Section: Introductionmentioning

confidence: 99%

“…Recently Sjöqvist et al have provided a new description for mixed state geometric phase in terms of quantum interferometry [11]. In a quantum interferometer a quantum system undergoes a series of unitary evolutions, after which the probability of finding the system in one of its eigenstates becomes an oscillatory function of some control parameter.…”

Section: Introductionmentioning

confidence: 99%

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Experimental measurement of mixed state geometric phase by quantum interferometry using NMR

Ghosh

Kumar

2006

Physics Letters A

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Geometric phase has been proposed as one of the promising methodologies to perform fault tolerant quantum computations. However, since decoherence plays a crucial role in such studies, understanding of mixed state geometric phase has become important. While mixed state geometric phase was first introduced mathematically by Uhlmann, recently Sjöqvist et al. [Phys. Rev. Lett. 85(14), 2845 (2000)] have described the mixed state geometric phase in the context of quantum interference and shown theoretically that the visibility as well as the shift of the interference pattern are functions of geometric phase and the purity of the mixed state. Here we report the first experimental study of the dependence of interference visibility and shift of the interference pattern on the mixed state geometric phase by Nuclear Magnetic Resonance.

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“…Therefore, the interference pattern given by Eq.7 takes the following form for a mixed input spin state [11],…”

Section: Theory Quantum Interferencementioning

confidence: 99%

“…As the phase shifter and the unitary operator 'U' are path specific, they are represented by two controlled operations, together given by [11],…”

Section: Theory Quantum Interferencementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Experimental measurement of mixed state geometric phase by quantum interferometry using NMR

Ghosh

Kumar

2006

Physics Letters A

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“…It has also brought out the relevance of the Bargmann invariants for geometric phase theory [11]. While some attempts have been made to define geometric phases for mixed state evolution [12][13][14][15], the emphasis at the basic level has been on pure states.…”

Section: Introductionmentioning

confidence: 99%

A classical optical approach to the ‘non-local Pancharatnam-like phases’ in Hanbury-Brown–Twiss correlations

2017

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We examine a recent proposal to show the presence of nonlocal Pancharatnam type geometric phases in a quantum mechanical treatment of intensity interferometry measurements upon inclusion of polarizing elements in the setup. It is shown that a completely classical statistical treatment of such effects is adequate for practical purposes. Further we show that the phase angles that appear in the correlations, while at first sight appearing to resemble Pancharatnam phases in their mathematical structure, cannot actually be interpreted in that manner. We also describe a simpler Mach-Zehnder type setup where similar effects can be observed without use of the paraxial approximation.

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Berry phase of two atoms in the same quantized light field

Liang¹,

Zhang²,

Yuan³

2007

Ann. Phys.

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The Berry phase of two atoms exposed to the same quantized light field has been studied. The interaction between each atom and the light field obeys the Jaynes-Cummings model. Due to the quantization of the light field, the interaction Hamiltonians for the two atoms interacting with the field do not commute with each other, which induces new parts in the Berry phase. Meanwhile, there appears a phase which doesn't exist in the classical regime and is purely induced by the field quantization.

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Geometric Phases for Mixed States in Interferometry

Cited by 557 publications

References 25 publications

Experimental measurement of mixed state geometric phase by quantum interferometry using NMR

Experimental measurement of mixed state geometric phase by quantum interferometry using NMR

A classical optical approach to the ‘non-local Pancharatnam-like phases’ in Hanbury-Brown–Twiss correlations

Berry phase of two atoms in the same quantized light field

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