Physical Review Letters

Fringe Visibility and Which-Way Information in an Atom Interferometer

Stephan Dürr, T. Nonn, Gerhard Rempe

Published Dec 28, 1998• 204 citations

Abstract

We experimentally investigate the reduction of the fringe visibility in an atom interferometer due to the storage of which-way information. We focus on the case of incomplete which-way information and use the distinguishability $D$ to quantify how much information is stored. For a given value of $D$, the fringe visibility $V$ is limited by the duality relation ${D}^{2}{+V}^{2}\ensuremath{\le}1$. We have measured $D$ and $V$ independently. Combining the results, we find good agreement with the duality relation.

DOI: 10.1103/physrevlett.81.5705

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Physical Review Letters

Fringe Visibility and Which-Way Information in an Atom Interferometer

Stephan Dürr, T. Nonn, Gerhard Rempe

Published Dec 28, 1998• 204 citations

Publisher

Abstract

D

to quantify how much information is stored. For a given value of

D

, the fringe visibility

V

is limited by the duality relation

{D}^{2}{+V}^{2}\ensuremath{\le}1

. We have measured

D

and

V

independently. Combining the results, we find good agreement with the duality relation.

DOI: 10.1103/physrevlett.81.5705

Related papers

Interference and partial which-way information: A quantitative test of duality in two-atom resonance

Yonatan Abranyos, Matthias Jakob, János A. Bergou

We propose for the experimental verification of an inequality concerning wave-particle duality by Englert [Phys. Rev. Lett. 77, 2154 (1996)] relating (or setting) an upper limit on distinguishability and visibility in a two-way interferometer. The inequality, quantifies the concept of wave-particle duality. The considered two-way interferometer is a Young's double-slit experiment involving two four-level atoms and is a slightly modified version of that of the recent experiment by Eichmann et al. [Phys. Rev. Lett. 70, 2359 (1993)]. The fringe visibility depends on the detected polarization direction of the scattered light and a read out of the internal state of one of the two atoms provides a partial which-way information.We propose for the experimental verification of an inequality concerning wave-particle duality by Englert [Phys. Rev. Lett. 77, 2154 (1996)] relating (or setting) an upper limit on distinguishability and visibility in a two-way interferometer. The inequality, quantifies the concept of wave-particle duality. The considered two-way interferometer is a Young's double-slit experiment involving two four-level atoms and is a slightly modified version of that of the recent experiment by Eichmann et al. [Phys. Rev. Lett. 70, 2359 (1993)]. The fringe visibility depends on the detected polarization direction of the scattered light and a read out of the internal state of one of the two atoms provides a partial which-way information.

Physical Review ADec 8, 19998 citations

Fringe Visibility and Which-Way Information: An Inequality

Berthold‐Georg Englert

Physical Review LettersSep 9, 1996817 citations

Hierarchy of inequalities for quantitative duality

Jesús Martínez-Linares

We derive different relations quantifying duality in a generic two-way interferometer. These relations set different upper bounds to the visibility $\mathcal{V}$ of the fringes measured at the output port of the interferometer. A hierarchy of inequalities is presented which exhibits the influence of the availability to the experimenter of different sources of which-way information contributing to the total distinguishability $\mathcal{D}$ of the ways. For mixed states and unbalanced interferometers an inequality is derived, ${\mathcal{V}}^{2}+{\ensuremath{\Xi}}^{2}\ensuremath{\le}1$, which can be more stringent than the one associated with the distinguishability $({\mathcal{V}}^{2}+{\mathcal{D}}^{2}\ensuremath{\le}1)$.We derive different relations quantifying duality in a generic two-way interferometer. These relations set different upper bounds to the visibility $\mathcal{V}$ of the fringes measured at the output port of the interferometer. A hierarchy of inequalities is presented which exhibits the influence of the availability to the experimenter of different sources of which-way information contributing to the total distinguishability $\mathcal{D}$ of the ways. For mixed states and unbalanced interferometers an inequality is derived, ${\mathcal{V}}^{2}+{\ensuremath{\Xi}}^{2}\ensuremath{\le}1$, which can be more stringent than the one associated with the distinguishability $({\mathcal{V}}^{2}+{\mathcal{D}}^{2}\ensuremath{\le}1)$.

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Quantum which-way information and fringe visibility when the detector is entangled with an ancilla

J. Prabhu Tej, A. R. Usha Devi, H. S. Karthik +2 more

Quantum-mechanical wave-particle duality is quantified in terms of a trade-off relation between the fringe visibility and the which-way distinguishability in an interference experiment. This relation was recently generalized by Banaszek et al. [Nat. Commun. 4, 2594 (2013)] when the particle is equipped with an internal degree of freedom such as spin. Here, we extend the visibility-distinguishability trade-off relation to quantum interference of a particle possessing an internal degree of freedom, when the which-way detector state is entangled with an ancillary system. We introduce an extended which-way distinguishability ${\mathcal{D}}_{E}$ and the associated extended fringe visibility ${\mathcal{V}}_{E}$ , satisfying the inequality ${\mathcal{D}}_{E}^{2}+{\mathcal{V}}_{E}^{2}\ensuremath{\le}1$ in this scenario. We illustrate, with the help of three specific examples, that while the which-way information inferred solely from the detector state (without ancilla) vanishes, the extended distinguishability retrievable via measurements on the detector-ancilla entangled state is nonzero. Furthermore, in all the three examples, the extended visibility and the generalized visibility (which was introduced by Banaszek et al.) match identically with each other.Quantum-mechanical wave-particle duality is quantified in terms of a trade-off relation between the fringe visibility and the which-way distinguishability in an interference experiment. This relation was recently generalized by Banaszek et al. [Nat. Commun. 4, 2594 (2013)] when the particle is equipped with an internal degree of freedom such as spin. Here, we extend the visibility-distinguishability trade-off relation to quantum interference of a particle possessing an internal degree of freedom, when the which-way detector state is entangled with an ancillary system. We introduce an extended which-way distinguishability ${\mathcal{D}}_{E}$ and the associated extended fringe visibility ${\mathcal{V}}_{E}$, satisfying the inequality ${\mathcal{D}}_{E}^{2}+{\mathcal{V}}_{E}^{2}\ensuremath{\le}1$ in this scenario. We illustrate, with the help of three specific examples, that while the which-way information inferred solely from the detector state (without ancilla) vanishes, the extended distinguishability retrievable via measurements on the detector-ancilla entangled state is nonzero. Furthermore, in all the three examples, the extended visibility and the generalized visibility (which was introduced by Banaszek et al.) match identically with each other.

arXiv:1404.6065Physical Review AJun 18, 20144 citations

“Quality” of a which-way detector

Jesús Martínez-Linares, David A. Harmin

We introduce a measure $\mathcal{Q}$ of the ``quality'' of a quantum which-way detector, which characterizes its intrinsic ability to extract which-way information in an asymmetric two-way interferometer. The ``quality'' $\mathcal{Q}$ allows one to separate the contribution to the distinguishability of the ways arising from the quantum properties of the detector from the contribution stemming from a priori which-way knowledge available to the experimenter, which can be quantified by a predictability parameter $\mathcal{P}.$ We provide an inequality relating these two sources of which-way information to the value of the fringe visibility displayed by the interferometer. We show that this inequality is an expression of duality, allowing one to trace the loss of coherence to the two reservoirs of which-way information represented by $\mathcal{Q}$ and $\mathcal{P}.$ Finally, we illustrate the formalism with the use of a quantum logic gate: the symmetric quanton-detecton system (SQDS). The SQDS can be regarded as two qubits trying to acquire which-way information about each other. The SQDS will provide an illustrating example of the reciprocal effects induced by duality between system and which-way detector.We introduce a measure $\mathcal{Q}$ of the ``quality'' of a quantum which-way detector, which characterizes its intrinsic ability to extract which-way information in an asymmetric two-way interferometer. The ``quality'' $\mathcal{Q}$ allows one to separate the contribution to the distinguishability of the ways arising from the quantum properties of the detector from the contribution stemming from a priori which-way knowledge available to the experimenter, which can be quantified by a predictability parameter $\mathcal{P}.$ We provide an inequality relating these two sources of which-way information to the value of the fringe visibility displayed by the interferometer. We show that this inequality is an expression of duality, allowing one to trace the loss of coherence to the two reservoirs of which-way information represented by $\mathcal{Q}$ and $\mathcal{P}.$ Finally, we illustrate the formalism with the use of a quantum logic gate: the symmetric quanton-detecton system (SQDS). The SQDS can be regarded as two qubits trying to acquire which-way information about each other. The SQDS will provide an illustrating example of the reciprocal effects induced by duality between system and which-way detector.

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2003 An interferometric complementarity experiment in a bulk nuclear magnetic resonance ensemble

Xinhua Peng, Xiwen Zhu, Ximing Fang +3 more

We have experimentally demonstrated the interferometric complementarity, which relates the distinguishability D quantifying the amount of which-way (WW) information to the fringe visibility V characterizing the wave feature of a quantum entity, in a bulk ensemble by Nuclear Magnetic Resonance (NMR) techniques. We primarily concern on the intermediate cases: partial fringe visibility and incomplete WW information. We define D by an alternative formalism and investigate the relation between D and entanglement. By measuring D and V independently, it turns out that the duality relation D 2 + V 2 = 1 holds for pure quantum states of the markers.We have experimentally demonstrated the interferometric complementarity, which relates the distinguishability D quantifying the amount of which-way (WW) information to the fringe visibility V characterizing the wave feature of a quantum entity, in a bulk ensemble by Nuclear Magnetic Resonance (NMR) techniques. We primarily concern on the intermediate cases: partial fringe visibility and incomplete WW information. We define D by an alternative formalism and investigate the relation between D and entanglement. By measuring D and V independently, it turns out that the duality relation D 2 + V 2 = 1 holds for pure quantum states of the markers.

Jan 31, 200218 citations

D

to quantify how much information is stored. For a given value of

D

, the fringe visibility

V

is limited by the duality relation

{D}^{2}{+V}^{2}\ensuremath{\le}1

. We have measured

D

and

V

independently. Combining the results, we find good agreement with the duality relation.

We derive different relations quantifying duality in a generic two-way interferometer. These relations set different upper bounds to the visibility

\mathcal{V}

of the fringes measured at the output port of the interferometer. A hierarchy of inequalities is presented which exhibits the influence of the availability to the experimenter of different sources of which-way information contributing to the total distinguishability

\mathcal{D}

of the ways. For mixed states and unbalanced interferometers an inequality is derived, ${\mathcal{V}}^{2}+{\ensuremath{\Xi}}^{2}\ensuremath{\le}1$, which can be more stringent than the one associated with the distinguishability $({\mathcal{V}}^{2}+{\mathcal{D}}^{2}\ensuremath{\le}1)$.

{\mathcal{D}}_{E}

and the associated extended fringe visibility

{\mathcal{V}}_{E}

, satisfying the inequality ${\mathcal{D}}_{E}^{2}+{\mathcal{V}}_{E}^{2}\ensuremath{\le}1$ in this scenario. We illustrate, with the help of three specific examples, that while the which-way information inferred solely from the detector state (without ancilla) vanishes, the extended distinguishability retrievable via measurements on the detector-ancilla entangled state is nonzero. Furthermore, in all the three examples, the extended visibility and the generalized visibility (which was introduced by Banaszek et al.) match identically with each other.

We introduce a measure

\mathcal{Q}

of the ``quality'' of a quantum which-way detector, which characterizes its intrinsic ability to extract which-way information in an asymmetric two-way interferometer. The ``quality''

\mathcal{Q}

allows one to separate the contribution to the distinguishability of the ways arising from the quantum properties of the detector from the contribution stemming from a priori which-way knowledge available to the experimenter, which can be quantified by a predictability parameter

\mathcal{P}.

We provide an inequality relating these two sources of which-way information to the value of the fringe visibility displayed by the interferometer. We show that this inequality is an expression of duality, allowing one to trace the loss of coherence to the two reservoirs of which-way information represented by

\mathcal{Q}

and

\mathcal{P}.

Finally, we illustrate the formalism with the use of a quantum logic gate: the symmetric quanton-detecton system (SQDS). The SQDS can be regarded as two qubits trying to acquire which-way information about each other. The SQDS will provide an illustrating example of the reciprocal effects induced by duality between system and which-way detector.