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Physical Review A

Complementarity and quantum erasure with entangled-photon states

Tedros Tsegaye, Gunnar G. Bjork, Mete Atatüre, Alexander V. Sergienko, Bahaa E. A. Saleh, Malvin Carl Teich

Published Aug 18, 2000• 23 citations
Publisher

Abstract

A quantum-erasure experiment was performed on superposition states of two photons in either of two spatiotemporal modes. Symmetrical tapping of energy from the two-mode state creates a four-mode entangled state. A direct measurement of one photon in two of the modes reveals the path of the second one, thereby eliminating the possibility of observing interference between the two remaining modes. It is shown that a unitary rotation of one of the two-mode states erases the path information; as a consequence, the visibility of the other two-mode state can be resurrected.

DOI
10.1103/physreva.62.032106

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A quantum-erasure experiment was performed on superposition states of two photons in either of two spatiotemporal modes. Symmetrical tapping of energy from the two-mode state creates a four-mode entangled state. A direct measurement of one photon in two of the modes reveals the path of the second one, thereby eliminating the possibility of observing interference between the two remaining modes. It is shown that a unitary rotation of one of the two-mode states erases the path information; as a consequence, the visibility of the other two-mode state can be resurrected.
We present various experiments demonstrating the mutual exclusivity of observing interference and which-path information, as demanded by Bohr's complementarity principle. Using photon pairs created in parametric down-conversion, no which-path measurements need to be performed on the interfering photon itself. Instead the other photon can be used to introduce distinguishability, which consequently destroys interference. However, a suitable measurement erases this distinguishability and interference can be recovered.
A quantum eraser is proposed that operates in a domain that does not have any classical counterpart. This quantum eraser utilizes the complementary aspect between entanglement and single-partite properties of composite quantum systems. Consequently, in contrast to the duality of visibility and which-path information which establish features of single quantum systems, here, properties of composite quantum systems are considered. In composite quantum systems entanglement might emerge which is of genuine quantum origin. This nonclassical correlation mutually exclude the single-partite properties of the subsystems of the composite quantum system. The single-partite properties can be describes by wave- and particle properties, i.e. the standard wave-particle duality. Remarkably, entanglement can be considered as a resource for observables that do not exist in classical physics. In a bipartite photon system, this observable is the two-particle visibility which describes the phase relations that are shared between both photons of the composite system. The complementary aspect between two-particle visibility and single-partite properties of the subsystems prevents us from the observation of single-partite properties in an entangled biphoton system. The quantum eraser erases the two-partite visibility and retrieves single-partite properties in form of single-particle visibility for both of the two photons. Thus, both observables contain phase information giving rise to interference effects. Here, complementarity is explicitly enforced by entanglement in a quantitative manner.
We have observed an effect known as a quantum eraser, using a setup similar to one previously employed to demonstrate a violation of Bell's inequalities. In this effect, an interfering system is first rendered incoherent by making the alternate Feynman paths which contribute to the overall process distinguishable; with our apparatus this is achieved by placing a half wave plate in one arm of a Hong-Ou-Mandel interferometer so as to rotate the polarization of the light in that arm by 90\ifmmode^\circ\else\textdegree\fi{}. This adds information to the system, in that polarization is a new parameter which serves to label the path of a given photon, even after a recombining beam splitter. The quantum ``eraser'' removes this information from the state vector, after the output port of the interferometer, but in time to cause interference effects to reappear upon coincidence detection. For this purpose, we use two polarizers in front of our detectors. We present experimental results showing how the degree of erasure (which determines the visibility of the interference) depends on the relative orientation of the polarizers, along with theoretical curves. In addition, we show how this procedure may do more than merely erase, in that the act of ``pasting together'' two previously distinguishable paths can introduce a new relative phase between them.
We describe a nonlocal method for generating entangled coherent states of a two-mode field wherein the field modes never meet. The proposed method is an extension of an earlier proposal [C. C. Gerry, Phys. Rev. A 59, 4095 (1999)] for the generation of superpositions of coherent states. A single photon injected into a Mach-Zehnder interferometer with cross-Kerr media in both arms coupling with two external fields in coherent states produces entangled coherent states upon detection at one of the output ports. We point out that our proposal can be alternatively viewed as a ``which path'' experiment, and in the case of only one external field, we describe the implementation of a quantum eraser.
Abstract The phenomenon of quantum erasure has shed light on the nature of wave-particle duality and quantum complementarity. A number of quantum erasers have been realized using the far-field diffraction of photons from a Young double-slit apparatus. By marking the path of a photon using an additional degree of freedom, the usual Young interference pattern is destroyed. An appropriate measurement of the system marking the photon’s path allows one to recover the interference pattern. Here quantum erasure is considered in the context of near-field diffraction. To observe interference in the near-field requires the use of two periodic wave functions, so that the usual ‘which way’ marker then becomes a ‘which-wave function’ marker. We determine the propagation distances for which quantum erasure, or more generally the observation of interference between the two periodic wave functions, can be observed. The meaning of wave and particle-like properties in this scenario is discussed. These results could lead to quantum eraser experiments with material particles, for which interference effects are more readily observed in the near-field rather than the far-field.