© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:1506.08323 · Physical Review A

Measurement-assisted Landau-Zener transitions

Alexander Nikolaevich Pechen, Anton Sergeevich Trushechkin

Published May 15, 2015• 43 citations

Abstract

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 nonselective 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.

DOI: 10.1103/physreva.91.052316

Related papers

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

Anna Novelli, Wolfgang Belzig, Abraham Nitzan

The time evolution and the asymptotic outcome of a Landau–Zener–Stueckelberg–Majorana (LZ) process under continuous weak non-selective measurement is analyzed. We compare two measurement protocols in which the populations of either the adiabatic or the non-adiabatic levels are (continuously and weakly) monitored. The weak measurement formalism, described using a Gaussian Kraus operator, leads to a time evolution characterized by a Markovian dephasing process, which, in the non-adiabatic measurement protocol is similar to earlier studies of LZ dynamics in a dephasing environment. Casting the problem in the language of measurement theory makes it possible for us to compare diabatic and adiabatic measurement scenarios, to consider engineered dephasing as a control device and to examine the manifestation of the Zeno effect under the different measurement protocols. In particular, under measurement of the non-adiabatic populations, the Zeno effect is manifested not as a freezing of the measured system in its initial state, but rather as an approach to equal asymptotic populations of the two diabatic states. This behavior can be traced to the way by which the weak measurement formalism behaves in the strong measurement limit, with a built-in relationship between measurement time and strength.

arXiv:1407.7154•New Journal of Physics•Jan 9, 2015•11 citations

Landau-Zener transition stabilized by the enhanced quantum Zeno effect in the bosonic system

Kai Wen, Tim Byrnes, Y. Yamamoto

We study the Landau-Zener transition with the quantum Zeno effect in an open dissipative system populated by a large number of bosons. Given the quantum Zeno effect is strong enough, both discrete and continuous quantum Zeno measurements are found to stabilize the Landau-Zener transition. Both the $σ^x$-type longitudinal relaxation and $σ^z$-type transverse relaxation in the bosonic system are analyzed as a model of continuous quantum Zeno measurements. While both of them improve the signal-to-noise ratio in terms of the ground state population, the $σ^x$-type relaxation can further boost measurement sensitivity and thus lead to a polynomial speedup with the number of bosons in the system. For a system that contains a large number of bosons such as in a Bose-Einstein condensate with more than $10^4$ bosons, this equates to several orders of magnitude speedup.

arXiv:1210.0173•Sep 30, 2012•0 citations

Quantum dynamics intervened by repeated nonselective measurements

Sergey N. Filippov

We derive the theory of open quantum system dynamics intervened by a series of nonselective measurements. We analyze the cases of time-independent and time-dependent Hamiltonian dynamics between the measurements and find the approximate master equation in the stroboscopic limit. We also consider a situation, in which the measurement basis changes in time, and illustrate it by nonselective measurements in the basis of diabatic states of the Landau–Zener model.

arXiv:1801.05160•International Journal of Quantum Information•Dec 1, 2017•0 citations

Quantum parameter estimation with the Landau-Zener transition

Jing Yang, Shengshi Pang, Andrew N. Jordan

We investigate the fundamental limits in precision allowed by quantum mechanics from Landau-Zener transitions, concerning Hamiltonian parameters. While the Landau-Zener transition probabilities depend sensitively on the system parameters, much more precision may be obtained using the acquired phase, quantified by the quantum Fisher information. This information scales with a power of the elapsed time for the quantum case, whereas it is time independent if the transition probabilities alone are used. We add coherent control to the system and increase the permitted maximum precision in this time-dependent quantum system. The case of multiple passes before measurement, Landau-Zener-Stueckelberg interferometry, is considered, and we demonstrate that proper quantum control can cause the quantum Fisher information about the oscillation frequency to scale as ${T}^{4}$, where $T$ is the elapsed time. These results are foundational for frequency standards and quantum clocks.

arXiv:1612.02390•Physical Review A•Aug 1, 2017•39 citations

Tunable Landau-Zener transitions in a spin-orbit-coupled Bose-Einstein condensate

Abraham J. Olson, Su-Ju Wang, Robert Niffenegger +3 more

The Landau-Zener (LZ) transition is one of the most fundamental phenomena in quantum dynamics. It describes nonadiabatic transitions between quantum states near an avoided crossing that can occur in diverse physical systems. Here we report experimental measurements and tuning of LZ transitions between the dressed eigenlevels of a Bose-Einstein condensate (BEC) that is synthetically spin-orbit (SO) coupled. We measure the transition probability as the BEC is accelerated through the SO avoided crossing and study its dependence on the coupling between the diabatic (bare) states, eigenlevel slope, and eigenstate velocity---the three parameters of the LZ model that are independently controlled in our experiments. Furthermore, we performed time-resolved measurements to demonstrate the breaking down of the spin-momentum locking of the spin-orbit-coupled BEC in the nonadiabatic regime, and we determined the diabatic switching time of the LZ transitions. Our observations show quantitative agreement with the LZ model and numerical simulations of the quantum dynamics in the quasimomentum space. The tunable LZ transition may be exploited to enable a spin-dependent atomtronic transistor.

arXiv:1310.1818•Physical Review A•Jul 17, 2014•175 citations

On the problem of maximizing the transition probability in an n-level quantum system using nonselective measurements

Alexander Nikolaevich Pechen, Nikolay Borisovich Ilin

We consider the problem of maximizing the probability of transition from a given initial state to a given final state for an n -level quantum system using nonselective quantum measurements. We find an estimate from below for the maximum of the transition probability for any fixed number of measurements and find the measured observables on which this estimate is attained.

Proceedings of the Steklov Institute of Mathematics•Aug 1, 2016•9 citations

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 nonselective 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.

The time evolution and the asymptotic outcome of a Landau–Zener–Stueckelberg–Majorana (LZ) process under continuous weak non-selective measurement is analyzed. We compare two measurement protocols in which the populations of either the adiabatic or the non-adiabatic levels are (continuously and weakly) monitored. The weak measurement formalism, described using a Gaussian Kraus operator, leads to a time evolution characterized by a Markovian dephasing process, which, in the non-adiabatic measurement protocol is similar to earlier studies of LZ dynamics in a dephasing environment. Casting the problem in the language of measurement theory makes it possible for us to compare diabatic and adiabatic measurement scenarios, to consider engineered dephasing as a control device and to examine the manifestation of the Zeno effect under the different measurement protocols. In particular, under measurement of the non-adiabatic populations, the Zeno effect is manifested not as a freezing of the measured system in its initial state, but rather as an approach to equal asymptotic populations of the two diabatic states. This behavior can be traced to the way by which the weak measurement formalism behaves in the strong measurement limit, with a built-in relationship between measurement time and strength.

We study the Landau-Zener transition with the quantum Zeno effect in an open dissipative system populated by a large number of bosons. Given the quantum Zeno effect is strong enough, both discrete and continuous quantum Zeno measurements are found to stabilize the Landau-Zener transition. Both the

σ^x

-type longitudinal relaxation and

σ^z

-type transverse relaxation in the bosonic system are analyzed as a model of continuous quantum Zeno measurements. While both of them improve the signal-to-noise ratio in terms of the ground state population, the

σ^x

-type relaxation can further boost measurement sensitivity and thus lead to a polynomial speedup with the number of bosons in the system. For a system that contains a large number of bosons such as in a Bose-Einstein condensate with more than

10^4

bosons, this equates to several orders of magnitude speedup.

We investigate the fundamental limits in precision allowed by quantum mechanics from Landau-Zener transitions, concerning Hamiltonian parameters. While the Landau-Zener transition probabilities depend sensitively on the system parameters, much more precision may be obtained using the acquired phase, quantified by the quantum Fisher information. This information scales with a power of the elapsed time for the quantum case, whereas it is time independent if the transition probabilities alone are used. We add coherent control to the system and increase the permitted maximum precision in this time-dependent quantum system. The case of multiple passes before measurement, Landau-Zener-Stueckelberg interferometry, is considered, and we demonstrate that proper quantum control can cause the quantum Fisher information about the oscillation frequency to scale as

{T}^{4}

, where

T

is the elapsed time. These results are foundational for frequency standards and quantum clocks.

The Landau-Zener (LZ) transition is one of the most fundamental phenomena in quantum dynamics. It describes nonadiabatic transitions between quantum states near an avoided crossing that can occur in diverse physical systems. Here we report experimental measurements and tuning of LZ transitions between the dressed eigenlevels of a Bose-Einstein condensate (BEC) that is synthetically spin-orbit (SO) coupled. We measure the transition probability as the BEC is accelerated through the SO avoided crossing and study its dependence on the coupling between the diabatic (bare) states, eigenlevel slope, and eigenstate velocity---the three parameters of the LZ model that are independently controlled in our experiments. Furthermore, we performed time-resolved measurements to demonstrate the breaking down of the spin-momentum locking of the spin-orbit-coupled BEC in the nonadiabatic regime, and we determined the diabatic switching time of the LZ transitions. Our observations show quantitative agreement with the LZ model and numerical simulations of the quantum dynamics in the quasimomentum space. The tunable LZ transition may be exploited to enable a spin-dependent atomtronic transistor.