Undetectable quantum transfer through a continuum

Jing, Ping; Yin, Yulong; Xu, Luting; Li, Xin-Qi; Yan, YiJing; Gurvitz, S. A.

doi:10.1016/j.physleta.2013.01.010

Physics Letters A

2013

DOI: 10.1016/j.physleta.2013.01.010

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Undetectable quantum transfer through a continuum

Ping Jing¹,

Yulong Yin²,

Luting Xu³

et al.

Abstract: We demonstrate that a quantum particle, initially prepared in a quantum well, can propagate through a reservoir with a continuous spectrum and reappear in a distant well without being registered in the reservoir. It is shown that such a passage through the reservoir takes place even if the latter is continuously monitored. We discuss a possible experimental realization of such a teleportation phenomenon in mesoscopic systems.

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Cited by 11 publications

(23 citation statements)

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“…Predictions based on the QT approach for this case are even more dramatic: The system can display the transition between these two localized states via the reservoir, although the latter is under continuous null-result monitoring [7]. This result is highly counterintuitive and is a clear contradiction of the Zeno effect.…”

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confidence: 93%

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Quantum transfer through a non-Markovian environment under frequent measurements and Zeno effect

Cao

et al. 2014

Phys. Rev. A

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We study transitions of a particle between two wells, separated by a reservoir, under the condition that the particle is not detected in the reservoir. Conventional quantum trajectory theory predicts that such no-result continuous measurement would not affect these transitions. We demonstrate that it holds only for Markovian reservoirs (infinite bandwidth ). In the case of finite , the probability of the particle's interwell transition is a function of the ratio /ν, where ν is the frequency of measurements. This scaling tells us that in the limit ν → ∞, the measurement freezes the initial state (the quantum Zeno effect), whereas for → ∞ it does not affect the particle's transition across the reservoir. The scaling is proved analytically by deriving a simple formula, which displays two regimes, with the Zeno effect and without the Zeno effect. It also supports a simple explanation of the Zeno effect entirely in terms of the energy-time uncertainty relation, with no explicit use of the projection postulate. Experimental tests of our predictions are discussed. It is well known that the unitary evolution of a quantum system is interrupted by measurement, so the subsequent evolution of a system depends on the measurement record. Frequent measurements with intervals t are of special interest. In the limit t → 0, they freeze the particle's motion (the quantum Zeno effect). This result is a consequence of the projection postulate applied to sequential measurements.The Zeno effect looks very surprising since it reveals the dynamical impact of the projection postulate on quantum motion. Instead, one can try to attribute the Zeno effect to the influence of the measurement devices. At first it seems as though this cannot be the case. Indeed, due to the interaction with detectors, the system acquires the energy ∼ / t, according to the energy-time uncertainty relation. As such, it is natural to expect an acceleration of the particle, instead of its freezing: the anti-Zeno effect [1]. Nevertheless, as demonstrated in this paper, the Zeno effect can be entirely attributed to the energy-time uncertainty relation, without the explicit use of the projection postulate. It would make the Zeno effect much less surprising and in fact quite expectable.The concept of continuous measurement is inherent in the quantum trajectory (QT) approach (informational evolution), which treats quantum motion based on the results of intermediate measurements [2]. It is therefore natural to investigate the Zeno-effect dynamics in this framework. A pronounced example of the informational evolution was proposed for a two-state system (qubit), coupled to a continuously monitored reservoir under the condition that no signal is registered there [3,4]. It was predicted that the qubit can change its state despite the null-result measurements. This was confirmed in experiment with a superconducting phase qubit measured via tunneling [5].In this paper we study a different arrangement, with two distant localized states, connected by a common reservoir under cont...

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confidence: 93%

“…In order to make the two setups fully equivalent, the PC detector should be placed symmetrically with respect to the dots. The system is described by Hamiltonian [6,7] where j = 1,2 and jr is tunneling coupling of the dot j with the reservoir. The states in the dots |1(2) are localized and the reservoir states |r are extended.…”

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confidence: 99%

Quantum transfer through a non-Markovian environment under frequent measurements and Zeno effect

Cao

et al. 2014

Phys. Rev. A

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“…However, in a recent study [2], where a double-dot connected by a continuum was considered, it was found that the second dot can affect the decay from the first dot via quantum interference, and finally lead to a formation of stationary bound state embedded in the continuum. In subsequent related studies [3,4], also concerning this dot-continuum-dot (DCD) system, it was demonstrated that the electron's motion through the continuum is very unusual, say, revealing an undetectable feature in the transfer process, and the information lost into the continuum can be retrieved without generating more disturbance.In the present work we consider inserting the DCD system into a transport configuration, as schematically shown by Fig. 1, which allows for an investigation for the behavior of continuous current through the DCD setup.…”

mentioning

confidence: 99%

“…1, which allows for an investigation for the behavior of continuous current through the DCD setup. Moreover, beyond the above DCD studies [2][3][4], where a wideband-limit (WBL) model was assumed for the central continuum, we will generalize our study to a finite-bandwidth Lorentzian spectrum (FBLS) for both the leads and the continuum. As a consequence, the transient transport process is highly non-Markovian, much stronger than in the WBL [5].…”

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Non-Markovian transmission through two quantum dots connected by a continuum

Cao¹,

Xu²,

Jian-Yu³

et al. 2012

Physics Letters A

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We consider a transport setup containing a double-dot connected by a continuum. Via an exact solution of the time-dependent Schrödinger equation, we demonstrate a highly non-Markovian quantum-coherence-mediated transport through this dot-continuum-dot (DCD) system, which is in contrast with the common premise since in typical case a quantum particle does not reenter the system of interest once it irreversibly decayed into a continuum (such as the spontaneous emission of a photon). We also find that this DCD system supports an unusual steady state with unequal source and drain currents, owing to electrons irreversibly entering the continuum and floating there.PACS numbers: 03.65. Yz, Coupling of a finite-size system to a reservoir with continuum energy spectrum is relevant to many fundamental issues of physics, e.g., the emergence of classicality from a quantum world [1], and the origin of irreversibility in statistical physics. Simple example of such type of coupling can be a small system, with discrete states, coupled to a continuum in terms of quantum tunneling.In most cases, coupling with a continuum would result in an irreversible decay of the discrete state, with the particle never coming back, such as the spontaneous emission of photon from an atom. However, in a recent study [2], where a double-dot connected by a continuum was considered, it was found that the second dot can affect the decay from the first dot via quantum interference, and finally lead to a formation of stationary bound state embedded in the continuum. In subsequent related studies [3,4], also concerning this dot-continuum-dot (DCD) system, it was demonstrated that the electron's motion through the continuum is very unusual, say, revealing an undetectable feature in the transfer process, and the information lost into the continuum can be retrieved without generating more disturbance.In the present work we consider inserting the DCD system into a transport configuration, as schematically shown by Fig. 1, which allows for an investigation for the behavior of continuous current through the DCD setup. Moreover, beyond the above DCD studies [2][3][4], where a wideband-limit (WBL) model was assumed for the central continuum, we will generalize our study to a finite-bandwidth Lorentzian spectrum (FBLS) for both the leads and the continuum. As a consequence, the transient transport process is highly non-Markovian, much stronger than in the WBL [5]. Particularly, associated with the peculiar DCD setup, we will discuss and uncover other features in relation with the coherence-mediated transfer and electron accumulation (floating) in the continuum, basing both on an exact treatment for the non-Markovian transport. The issue of non-Markovian transport through quantum dots has received considerable attention in the past years [6-13], * Electronic address: lixinqi@bnu.edu.cn where the non-Markovian transient dynamics are usually manifested in the current noise spectrum or in terms of full counting statistics. Moreover, exploiting the nature of non-Mark...

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Formation of defects during fullerene bombardment and repair of vacancy defects in graphene

Luo

Gao

et al. 2019

J Mater Sci

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Undetectable quantum transfer through a continuum

Cited by 11 publications

References 18 publications

Quantum transfer through a non-Markovian environment under frequent measurements and Zeno effect

Quantum transfer through a non-Markovian environment under frequent measurements and Zeno effect

Non-Markovian transmission through two quantum dots connected by a continuum

Formation of defects during fullerene bombardment and repair of vacancy defects in graphene

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