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Physical Review A

Zeno effect in degree of polarization of a single photon or quantum-state purity of a spin-1/2 system

Alfredo Luis, Isabel Gonzalo, Miguel A. Porras

Published Jun 20, 2013• 3 citations
Publisher

Abstract

We describe a version of the Zeno effect where the monitored physical property cannot be represented by a standard operator in the system space and the evolution to be prevented by observation is not unitary. This is the case of quantum-state purity of a spin-1/2 system, which is equivalent to the degree of polarization of a single photon. By a suitable embedding of the system (say, a single photon) in an enlarged space of a pair of photons, pure and fully mixed components lead to orthogonal subspaces, with lack of purity becoming equivalent to entanglement. By imposing desirable properties the representation of the system in the enlarged space is unique. We show that the Zeno effect is possible, and experimentally feasible, in the enlarged space. The peculiarity that photons in identical polarization states are involved in pairs to observe the dynamics of each photon allows us to refer it as the self-Zeno effect or Narcissus effect.

DOI
10.1103/physreva.87.064102

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We describe a version of the Zeno effect where the monitored physical property cannot be represented by a standard operator in the system space and the evolution to be prevented by observation is not unitary. This is the case of quantum-state purity of a spin-1/2 system, which is equivalent to the degree of polarization of a single photon. By a suitable embedding of the system (say, a single photon) in an enlarged space of a pair of photons, pure and fully mixed components lead to orthogonal subspaces, with lack of purity becoming equivalent to entanglement. By imposing desirable properties the representation of the system in the enlarged space is unique. We show that the Zeno effect is possible, and experimentally feasible, in the enlarged space. The peculiarity that photons in identical polarization states are involved in pairs to observe the dynamics of each photon allows us to refer it as the self-Zeno effect or Narcissus effect.
The quantum Zeno effect of a single system is the effect of a series of measurements on the unitary time evolution of the system and on the ability to monitor this time evolution using the measurement results. This effect is shown to be equivalent to that of the indetermination of the quantum state of a single system [Phys. Rev. Lett. 74, 4106 (1995)], in which one considers the statistics of the results of a series of measurements performed on a single system, with no time evolution in between successive measurements.
The fragility of quantum coherence fundamentally limits the scalability of quantum technologies, as unavoidable environmental interactions induce decoherence and rapidly degrade quantum properties. The Quantum Zeno Effect offers a powerful route to suppress quantum evolution and protect coherence through frequent measurements, irrespective of the underlying dynamics. However, existing implementations require prior knowledge of the quantum state, severely restricting their applicability. Here we introduce a state- and dynamics-independent protection protocol embedding the system in a larger Hilbert space, temporarily swapping the quantum information from its original degree of freedom to a decoherence-free ancillary one. We experimentally validate the protocol on a quantum optical platform, demonstrating robust preservation of coherence and purity for arbitrary polarization qubits under decoherence, thereby enabling the universal safeguarding of unknown quantum states.
In this work we theoretically consider quantum Zeno effect for entangled (correlated) quantum states. (Our physical systems and calculations are simpler than it is case in remarkable work on entanglement protection via Zeno effect by Maniscalco et all. But Maniscalco et all and our final conclusions are the same.) Firstly, we demonstrate well-known quantum Zeno effect by frequent decay detection for single, simple, two-level quantum system, with stable, ground quantum state and one non-stable, excited quantum state which can decay, by photon emission, in the ground state. (In this case, by frequent decay detections, system stands in the excited state.) Further, we consider single photon with energy equivalent to energy difference between excited and ground energy level of mentioned system. After interaction with a half-silvered mirror, mentioned photon is in a quantum superposition of the reflected and transmitted quantum state or trajectory. Mentioned trajectories are directed toward two identical, but distant, mentioned simple two-level systems both of which are initially (before interaction with photon) in ground state. Immediately after interaction with photon (photon absorption) two two-level systems are described by entangled (correlated) quantum state ( (excited, ground) + (ground, excited) , symbolically). We prove that in this case, by frequent decay detections on both systems, mentioned two two-level systems are described by initial entangled (correlated) quantum state ( (excited, ground) +(ground, excited)).
We present a scheme for experimentally observing the quantum Zeno effect using the quantum-nondemolition measurement recently proposed by Brune et al. [Phys. Rev. Lett. 65, 976 (1990)]. The Zeno effect refers to the freezing of the (unitary) free dynamics of a system by rapid measurements. We generalize the Zeno effect to be any change in the survival probability of an initial state induced by very rapid measurements, when such measurements are the dominant source of fluctuations in the system. We derive a master equation for the evolution of a cavity mode when the photon number is monitored by this method. This equation describes a phase-diffusion process. We propose that this measurement scheme be used to monitor the exchange of a single photon between the cavity and a single Rydberg atom. We show that for very rapid monitoring the free oscillation of the atomic inversion is disrupted and the atom can be trapped close to the initial excited state. This is the quantum Zeno effect.
The quantum Zeno effect reveals that continuous observation of a quantum system can significantly alter its evolution. Here, we present a method for establishing polarization entanglement between two initially unentangled photons in coupled waveguides via the quantum Zeno effect. We support our analytical investigation with numerical simulations of the underlying Schrodinger equation describing the system. Further, we extend our technique to three coupled waveguides in a planar configuration and determine the parameters required to generate three-qubit W-states. In contrast to existing schemes based on a vacuum and single-photon encoding, the polarization encoding in our approach is compatible with quantum information protocols that remove photon loss through post-selection. Our findings offer a powerful quantum state engineering approach for photonic quantum information technologies.
The evolution of a quantum system is supposed to be impeded by measurement of an involved observable. This effect has been proven indistinguishable from the effect of dephasing the system's wave function, except in an individual quantum system. The coherent dynamics, on an optical E2 line, of a single trapped ion driven by light of negligible phase drift has been alternated with interrogations of the internal ion state. Retardation of the ion's nutation, equivalent to the quantum Zeno effect, is demonstrated in the statistics of sequences of probe-light scattering ''on'' and ''off'' detections, the latter representing back-action-free measurement.