Landau–Zener evolution under weak measurement: manifestation of the Zeno effect under diabatic and adiabatic measurement protocols

Novelli, Anna; Belzig, Wolfgang; Nitzan, Abraham

doi:10.1088/1367-2630/17/1/013001

Cited by 10 publications

(7 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this regime, if time instants of measurements are not well defined and it significantly affects the desired transition probability, then the optimal solution will be to perform only one measurement at the avoided crossing time instant. This measurement will increase the transition probability from almost zero to 1/2, which agrees with the analysis of the quantum Zeno effect in the LZ system based on weak measurements [62] and the analysis of the LZ dynamics under strong dephasing [63,64]. Generally, the formalism of continuous or weak measurements can be used if the duration of measurements is comparable to or larger than the intervals between the optimal time instants [65][66][67][68][69].…”

Section: Conclusion and Discussionsupporting

confidence: 77%

Measurement-assisted Landau-Zener transitions

Pechen

Трушечкин

2015

Phys. Rev. A

View full text Add to dashboard Cite

Nonselective quantum measurements, i.e., measurements without reading the results, are often considered as a resource for manipulating quantum systems. In this work, we investigate optimal acceleration of the Landau-Zener (LZ) transitions by non-selective quantum measurements. We use the measurements of a population of a diabatic state of the LZ system at certain time instants as control and find the optimal time instants which maximize the LZ transition. We find surprising nonmonotonic behavior of the maximal transition probability with increase of the coupling parameter when the number of measurements is large. This transition probability gives an optimal approximation to the fundamental quantum Zeno effect (which corresponds to continuous measurements) by a fixed number of discrete measurements. The difficulty for the analysis is that the transition probability as a function of time instants has a huge number of local maxima. We resolve this problem both analytically by asymptotic analysis and numerically by the development of efficient algorithms mainly based on the dynamic programming. The proposed numerical methods can be applied, besides this problem, to a wide class of measurement-based optimal control problems.Comment: 17 pages, 7 figure

show abstract

Section: Conclusion and Discussionsupporting

confidence: 77%

Measurement-assisted Landau-Zener transitions

Pechen

Трушечкин

2015

Phys. Rev. A

View full text Add to dashboard Cite

show abstract

“…Finally we would like to note that the treatment of continuous measurements in terms of an SME also leads to a Lindblad-type master equation, see (52), similarly as obtained in various recent publications [61][62][63][64] which are concerned with the definition of work and heat and the quest for fluctuation theorems in open quantum 15 In [58,60] the dynamics in the strong measurement regime is referred to as the quantum Zeno effect. In our work we reserve the latter term for the complete freezing of unitary dynamics achieved by repeated projective measurements discussed in section 2.…”

Section: Resultsmentioning

confidence: 72%

“…Also note that for our choice of parameters in figures 8 and 9, we are also in the strong measurement regime of κ > ∆/ for the LZ problem where the coherent dynamics rate ∆ is trumped by the measurement backaction. It is known [58][59][60] that for the LZ system under continuous measurement, the behaviour of single trajectory solutions of (49) goes from near unitary at very small measurement strength to the so-called "random-telegraph" dynamics at the strong measurement κ > ∆/ regime (In [58,60] the dynamics in the strong measurement regime is referred to as the quantum Zeno effect. In our work we reserve the latter term for the complete freezing of unitary dynamics achieved by repeated projective measurements discussed in section 2).…”

Section: Continuous Measurementsmentioning

confidence: 99%

“…Also note that for our choice of parameters in figures 8 and 9, we are also in the strong measurement regime of  κ Δ > for the LZ problem where the coherent dynamics rate Δ is trumped by the measurement backaction. It is known [58][59][60] that for the LZ system under continuous measurement, the behaviour of single trajectory solutions of (49) goes from near unitary at very small measurement strength to the so-called 'random-telegraph' dynamics at the strong measurement  κ Δ > regime 15 . The randomtelegraph behaviour is characterised by the population difference of diabatic states z σ 〈 〉remaining localised either at ±1 and undergoing rapid transitions between the two values at different times during the evolution (see discussion in section 3 B of [58]).…”

mentioning

confidence: 99%

See 1 more Smart Citation

Quantum fluctuation theorems and power measurements

2015

View full text Add to dashboard Cite

Work in the paradigm of the quantum fluctuation theorems of Crooks and Jarzynski is determined by projective measurements of energy at the beginning and end of the force protocol. In analogy to classical systems, we consider an alternative definition of work given by the integral of the supplied power determined by integrating up the results of repeated measurements of the instantaneous power during the force protocol. We observe that such a definition of work, in spite of taking account of the process dependence, has different possible values and statistics from the work determined by the conventional two energy measurement approach (TEMA). In the limit of many projective measurements of power, the system's dynamics is frozen in the power measurement basis due to the quantum Zeno effect leading to statistics only trivially dependent on the force protocol. In general the Jarzynski relation is not satisfied except for the case when the instantaneous power operator commutes with the total Hamiltonian at all times. We also consider properties of the joint statistics of powerbased definition of work and TEMA work in protocols where both values are determined. This allows us to quantify their correlations. Relaxing the projective measurement condition, weak continuous measurements of power are considered within the stochastic master equation formalism. Even in this scenario the power-based work statistics is in general not able to reproduce qualitative features of the TEMA work statistics.

show abstract

“…In a two-level system, the loss of phase coherence between two states can be described by a Lindblad operator proportional to the difference between the projectors on such states. In the prototypical cases, hereafter labeled a and b, dephasing takes place between the states that form either the diabatic or the adiabatic basis [25]:…”

Section: Introduction -mentioning

confidence: 99%

Landau-Zener Transition in a Continuously Measured Single-Molecule Spin Transistor

et al. 2017

View full text Add to dashboard Cite

We monitor the Landau-Zener dynamics of a single-ion magnet in a spin-transistor geometry. For increasing field-sweep rates, the spin reversal probability shows increasing deviations from that of a closed system. In the low-conductance limit, such deviations are shown to result from a dephasing process. In particular, the observed behaviors are succesfully simulated by means of an adiabatic master equation, with time averaged dephasing (Lindblad) operators. The time average is tentatively interpeted in terms of the finite time resolution of the continuous measurement. Introduction -The dynamics of a quantum system driven through an avoided level crossing represents a relevant problem in many physical contexts. In the simplest case, known as the Landau-Zener problem, the dynamics involves only two states, coupled by a constant tunneling term, and separated in energy by a gap that depends linearly on time. This problem was independently solved by different authors, who provided an analytical expression for the probability that the system eventually undergoes a spin reversal [1][2][3][4]. However, these results apply to the ideal case of an isolated quantum system. In realistic conditions, coupling to the environment tends to induce decoherence, both through elastic and inelastic processes. In fact, decoherence can affect the Landau-Zener dynamics in substantially different ways, depending on the environment composition (e.g., harmonic oscillators or spins), temperature, and on the presence or absence of memory effects [5][6][7][8][9][10]. Departures from a unitary evolution can also be induced by a measurement process, which presents deep conceptual and formal connections with decoherence [11][12][13]. In particular, a continuous measurement of the system tends to destroy the phase coherence between different eigenstates of the observable. Continuous measurements of single quantum objects have been investigated by electrical and optical means in mesoscopic [14][15][16][17] and atomic systems [18], respectively. Whether decoherence is induced by the coupling to a quantum environment or to a measuring apparatus, its effective character qualitatively depends on the interplay between such coupling and the interactions within the system [19], which can be explored and controlled by means of an external drive [20].

show abstract

Landau–Zener evolution under weak measurement: manifestation of the Zeno effect under diabatic and adiabatic measurement protocols

Cited by 10 publications

References 46 publications

Measurement-assisted Landau-Zener transitions

Measurement-assisted Landau-Zener transitions

Quantum fluctuation theorems and power measurements

Landau-Zener Transition in a Continuously Measured Single-Molecule Spin Transistor

Contact Info

Product

Resources

About