Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0404150 · Physical Review A

Stabilizing quantum metastable states in a time-periodic potential

Choon-Lin Ho, Chung‐Chieh Lee

Published Jan 7, 2005• 11 citations
arXivHTMLPDF

Abstract

Metastability of a particle trapped in a well with a time-periodically oscillating barrier is studied in the Floquet formalism. It is shown that the oscillating barrier causes the system to decay faster in general. However, avoided crossings of metastable states can occur with the less stable states crossing over to the more stable ones. If in the static well there exists a bound state, then it is possible to stabilize a metastable state by adiabatically increasing the oscillating frequency of the barrier so that the unstable state will eventually cross over to the stable bound state. It is also found that increasing the amplitude of the oscillating field may change a direct crossing of states into an avoided one.

DOI
10.1103/physreva.71.012102

Related papers

STABILIZING QUANTUM METASTABLE STATES IN A TIME-PERIODIC POTENTIAL

Choon-Lin Ho, Chung‐Chieh Lee

In this talk we present a model to demonstrate how time-periodic potential can be used to manipulate quantum metastability of a system. We study metastability of a particle trapped in a well with a time-periodically oscillating barrier in the Floquet formalism. It is shown that the oscillating barrier causes the system to decay faster in general. However, avoided crossings of metastable states can occur with the less stable states crossing over to the more stable ones. If in the static well there exists a bound state, then it is possible to stabilize a metastable state by adiabatically increasing the oscillating frequency of the barrier so that the unstable state eventually cross-over to the stable bound state. It is also found that increasing the amplitude of the oscillating field may change a direct crossing of states into an avoided one. Hence, one can manipulate the stability of different states in a quantum potential by a combination of adiabatic changes of the frequency and the amplitude of the oscillating barrier.

arXiv:0710.2205•International Journal of Modern Physics B•Sep 30, 2007•0 citations

Stabilizing quantum metastable states in a time-periodic potential

Choon-Lin Ho, Chung‐Chieh Lee

In this talk we present a model to demonstrate how time‐periodic potential can be used to manipulate quantum metastability of a system. We study metastability of a particle trapped in a well with a time‐periodically oscillating barrier in the Floquet formalism. It is shown that the oscillating barrier causes the system to decay faster in general. However, avoided crossings of metastable states can occur with the less stable states crossing over to the more stable ones. If in the static well there exists a bound state, then it is possible to stabilize a metastable state by adiabatically increasing the oscillating frequency of the barrier so that the unstable state eventually cross‐over to the stable bound state. It is also found that increasing the amplitude of the oscillating field may change a direct crossing of states into an avoided one. Hence, one can manipulate the stability of different states in a quantum potential by a combination of adiabatic changes of the frequency and the amplitude of the oscillating barrier.

AIP conference proceedings•Jan 1, 2006•0 citations

Oscillating potential well in the complex plane and the adiabatic theorem

Stefano Longhi

A quantum particle in a slowly changing potential well $V(x,t)=V(x\ensuremath{-}{x}_{0}(\ensuremath{\epsilon}t))$, periodically shaken in time at a slow frequency $\ensuremath{\epsilon}$, provides an important quantum mechanical system where the adiabatic theorem fails to predict the asymptotic dynamics over time scales longer than $\ensuremath{\sim}1/\ensuremath{\epsilon}$. Specifically, we consider a double-well potential $V(x)$ sustaining two bound states spaced in frequency by ${\ensuremath{\omega}}_{0}$ and periodically shaken in a complex plane. Two different spatial displacements ${x}_{0}(t)$ are assumed: the real spatial displacement ${x}_{0}(\ensuremath{\epsilon}t)=Asin(\ensuremath{\epsilon}t)$, corresponding to ordinary Hermitian shaking, and the complex one ${x}_{0}(\ensuremath{\epsilon}t)=A\ensuremath{-}Aexp(\ensuremath{-}i\ensuremath{\epsilon}t)$, corresponding to non-Hermitian shaking. When the particle is initially prepared in the ground state of the potential well, breakdown of adiabatic evolution is found for both Hermitian and non-Hermitian shaking whenever the oscillation frequency $\ensuremath{\epsilon}$ is close to an odd resonance of ${\ensuremath{\omega}}_{0}$. However, a different physical mechanism underlying nonadiabatic transitions is found in the two cases. For the Hermitian shaking, an avoided crossing of quasienergies is observed at odd resonances and nonadiabatic transitions between the two bound states, resulting in Rabi flopping, can be explained as a multiphoton resonance process. For the complex oscillating potential well, breakdown of adiabaticity arises from the appearance of Floquet exceptional points at exact quasienergy crossing.

arXiv:1710.04429•Physical Review A•Oct 2, 2017•7 citations

Dissipative quantum systems with a potential barrier. III. Steady state nonequilibrium flux and reaction rate

Joachim Ankerhold, Hermann Grabert

We study the real time dynamics of a dissipative quantum system in a metastable state which may decay by crossing a potential barrier. Starting from an initial state where the system is in thermal equilibrium on one side of the barrier, the time evolution of the density matrix is evaluated analytically in the semiclassical approximation for coordinates near the barrier top. In a region about a critical temperature ${\mathrm{T}}_{\mathrm{c}}$ large quantum fluctuations render the harmonic approximation of the potential insufficient and anharmonicities become essential. Accounting for non-Gaussian fluctuation modes, we show that the density matrix approaches a quasistationary state with a constant flux across the barrier. This extends our earlier results [Phys. Rev. E 51, 4267 (1995)] on the quantum generalization of the Kramers flux state to the region about ${\mathrm{T}}_{\mathrm{c}}$. By matching the flux state onto the equilibrium state on one side of the barrier, we determine the decay rate out of the metastable state. The rate constant shows a changeover from thermally activated decay to quantum tunneling for temperatures below ${\mathrm{T}}_{\mathrm{c}}$.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Feb 1, 1997•9 citations

Floquet analysis of the modulated two-mode Bose-Hubbard model

Gentaro Watanabe A, H. Mäkelä

We study the tunneling dynamics in a time-periodically modulated two-mode Bose-Hubbard model using Floquet theory. We consider situations where the system is in the self-trapping regime and either the tunneling amplitude, the interaction strength, or the energy difference between the modes is modulated. In the former two cases, the tunneling is enhanced in a wide range of modulation frequencies, while in the latter case the resonance is narrow. We explain this difference with the help of Floquet analysis. If the modulation amplitude is weak, the locations of the resonances can be found using the spectrum of the nonmodulated Hamiltonian. Furthermore, we use Floquet analysis to explain the coherent destruction of tunneling (CDT) occurring in a large-amplitude modulated system. Finally, we present two ways to create a NOON state (a superposition of $N$ particles in mode 1 with zero particles in mode 2 and vice versa). One is based on a coherent oscillation caused by detuning from a partial CDT. The other makes use of an adiabatic variation of the modulation frequency. This results in a Landau-Zener type of transition between the ground state and a NOON-like state.

arXiv:1203.2792•Physical Review A•May 17, 2012•21 citations

Sudden transition from a stable to an unstable harmonic trap as the adiabatic potential parameter is varied in a time-periodic harmonic trap

Nimrod Moiseyev

It has been shown already that when the harmonic trap is opened (or closed) as a function of time while keeping the adiabatic parameter $\ensuremath{\mu}=[d\ensuremath{\omega}(t)/dt]/{\ensuremath{\omega}}^{2}(t)$ fixed, a sharp transition from an oscillatory to a monotonic exponential dynamics occurs at $\ensuremath{\mu}=2$ [Uzdin, Dalla Torre, Kosloff, and Moiseyev, Phys. Rev. A 88, 022505 (2013)]. Here we show that by using time-dependent linear coordinate transformation the time-dependent Schr\"odinger equation with Hermitian time-dependent Hamiltonian is transformed into a time-dependent Schr\"odinger equation with a time-independent harmonic oscillator with the dimensionless frequency of $\sqrt{1\ensuremath{-}{(\ensuremath{\mu}/2)}^{2}}$. At $\ensuremath{\mu}=2$ a transition to a non-Hermitian Hamiltonian is obtained as the potential well is transformed to a parabolic potential barrier. While in a harmonic trap noninteracting particles have classical periodic motions, they are pushed apart exponentially in time as the potential well is suddenly transformed into a parabolic potential barrier in the new variable representation.

Physical Review A•Sep 30, 2013•4 citations
Metastability of a particle trapped in a well with a time-periodically oscillating barrier is studied in the Floquet formalism. It is shown that the oscillating barrier causes the system to decay faster in general. However, avoided crossings of metastable states can occur with the less stable states crossing over to the more stable ones. If in the static well there exists a bound state, then it is possible to stabilize a metastable state by adiabatically increasing the oscillating frequency of the barrier so that the unstable state will eventually cross over to the stable bound state. It is also found that increasing the amplitude of the oscillating field may change a direct crossing of states into an avoided one.
In this talk we present a model to demonstrate how time-periodic potential can be used to manipulate quantum metastability of a system. We study metastability of a particle trapped in a well with a time-periodically oscillating barrier in the Floquet formalism. It is shown that the oscillating barrier causes the system to decay faster in general. However, avoided crossings of metastable states can occur with the less stable states crossing over to the more stable ones. If in the static well there exists a bound state, then it is possible to stabilize a metastable state by adiabatically increasing the oscillating frequency of the barrier so that the unstable state eventually cross-over to the stable bound state. It is also found that increasing the amplitude of the oscillating field may change a direct crossing of states into an avoided one. Hence, one can manipulate the stability of different states in a quantum potential by a combination of adiabatic changes of the frequency and the amplitude of the oscillating barrier.
In this talk we present a model to demonstrate how time‐periodic potential can be used to manipulate quantum metastability of a system. We study metastability of a particle trapped in a well with a time‐periodically oscillating barrier in the Floquet formalism. It is shown that the oscillating barrier causes the system to decay faster in general. However, avoided crossings of metastable states can occur with the less stable states crossing over to the more stable ones. If in the static well there exists a bound state, then it is possible to stabilize a metastable state by adiabatically increasing the oscillating frequency of the barrier so that the unstable state eventually cross‐over to the stable bound state. It is also found that increasing the amplitude of the oscillating field may change a direct crossing of states into an avoided one. Hence, one can manipulate the stability of different states in a quantum potential by a combination of adiabatic changes of the frequency and the amplitude of the oscillating barrier.
A quantum particle in a slowly changing potential well $V(x,t)=V(x\ensuremath{-}{x}_{0}(\ensuremath{\epsilon}t))$, periodically shaken in time at a slow frequency $\ensuremath{\epsilon}$, provides an important quantum mechanical system where the adiabatic theorem fails to predict the asymptotic dynamics over time scales longer than $\ensuremath{\sim}1/\ensuremath{\epsilon}$. Specifically, we consider a double-well potential V(x)V(x)V(x) sustaining two bound states spaced in frequency by ${\ensuremath{\omega}}_{0}$ and periodically shaken in a complex plane. Two different spatial displacements x0(t){x}_{0}(t)x0​(t) are assumed: the real spatial displacement ${x}_{0}(\ensuremath{\epsilon}t)=Asin(\ensuremath{\epsilon}t)$, corresponding to ordinary Hermitian shaking, and the complex one ${x}_{0}(\ensuremath{\epsilon}t)=A\ensuremath{-}Aexp(\ensuremath{-}i\ensuremath{\epsilon}t)$, corresponding to non-Hermitian shaking. When the particle is initially prepared in the ground state of the potential well, breakdown of adiabatic evolution is found for both Hermitian and non-Hermitian shaking whenever the oscillation frequency $\ensuremath{\epsilon}$ is close to an odd resonance of ${\ensuremath{\omega}}_{0}$. However, a different physical mechanism underlying nonadiabatic transitions is found in the two cases. For the Hermitian shaking, an avoided crossing of quasienergies is observed at odd resonances and nonadiabatic transitions between the two bound states, resulting in Rabi flopping, can be explained as a multiphoton resonance process. For the complex oscillating potential well, breakdown of adiabaticity arises from the appearance of Floquet exceptional points at exact quasienergy crossing.
We study the real time dynamics of a dissipative quantum system in a metastable state which may decay by crossing a potential barrier. Starting from an initial state where the system is in thermal equilibrium on one side of the barrier, the time evolution of the density matrix is evaluated analytically in the semiclassical approximation for coordinates near the barrier top. In a region about a critical temperature Tc{\mathrm{T}}_{\mathrm{c}}Tc​ large quantum fluctuations render the harmonic approximation of the potential insufficient and anharmonicities become essential. Accounting for non-Gaussian fluctuation modes, we show that the density matrix approaches a quasistationary state with a constant flux across the barrier. This extends our earlier results [Phys. Rev. E 51, 4267 (1995)] on the quantum generalization of the Kramers flux state to the region about Tc{\mathrm{T}}_{\mathrm{c}}Tc​. By matching the flux state onto the equilibrium state on one side of the barrier, we determine the decay rate out of the metastable state. The rate constant shows a changeover from thermally activated decay to quantum tunneling for temperatures below Tc{\mathrm{T}}_{\mathrm{c}}Tc​.
We study the tunneling dynamics in a time-periodically modulated two-mode Bose-Hubbard model using Floquet theory. We consider situations where the system is in the self-trapping regime and either the tunneling amplitude, the interaction strength, or the energy difference between the modes is modulated. In the former two cases, the tunneling is enhanced in a wide range of modulation frequencies, while in the latter case the resonance is narrow. We explain this difference with the help of Floquet analysis. If the modulation amplitude is weak, the locations of the resonances can be found using the spectrum of the nonmodulated Hamiltonian. Furthermore, we use Floquet analysis to explain the coherent destruction of tunneling (CDT) occurring in a large-amplitude modulated system. Finally, we present two ways to create a NOON state (a superposition of NNN particles in mode 1 with zero particles in mode 2 and vice versa). One is based on a coherent oscillation caused by detuning from a partial CDT. The other makes use of an adiabatic variation of the modulation frequency. This results in a Landau-Zener type of transition between the ground state and a NOON-like state.
It has been shown already that when the harmonic trap is opened (or closed) as a function of time while keeping the adiabatic parameter $\ensuremath{\mu}=[d\ensuremath{\omega}(t)/dt]/{\ensuremath{\omega}}^{2}(t)$ fixed, a sharp transition from an oscillatory to a monotonic exponential dynamics occurs at $\ensuremath{\mu}=2$ [Uzdin, Dalla Torre, Kosloff, and Moiseyev, Phys. Rev. A 88, 022505 (2013)]. Here we show that by using time-dependent linear coordinate transformation the time-dependent Schr\"odinger equation with Hermitian time-dependent Hamiltonian is transformed into a time-dependent Schr\"odinger equation with a time-independent harmonic oscillator with the dimensionless frequency of $\sqrt{1\ensuremath{-}{(\ensuremath{\mu}/2)}^{2}}$. At $\ensuremath{\mu}=2$ a transition to a non-Hermitian Hamiltonian is obtained as the potential well is transformed to a parabolic potential barrier. While in a harmonic trap noninteracting particles have classical periodic motions, they are pushed apart exponentially in time as the potential well is suddenly transformed into a parabolic potential barrier in the new variable representation.