The Demkov-Kunike (DK) model, characterized by a time-dependent Rabi coupling $J\phantom{\rule{0.16em}{0ex}}\text{sech}(t/T)$ and on-site detuning ${\mathrm{\ensuremath{\Delta}}}_{0}+{\mathrm{\ensuremath{\Delta}}}_{1}tanh(t/T)$, has one of the most general forms of an exactly solvable two-state quantum system and therefore it provides a paradigm for coherent manipulations of a qubit's quantum state. Despite its extensive application in noise-free cases, the exploration of the noisy DK model remains limited. Here we extend the coherent DK model to take into account a noisy coupling term $J\ensuremath{\rightarrow}{J}_{\text{noisy}}(t)$. We consider colored Markovian noise sources represented by telegraph noise and Gaussian noise. We present exact solutions for the survival probability ${Q}_{\text{DK}}^{\text{noisy}}$ of the noisy DK model, namely, the probability of the system to remain in its initial state. For slow telegraph noise, we identify parameter regimes where the survival probability ${Q}_{\text{DK}}^{\text{noisy}}$ is suppressed rather than enhanced by noise. In contrast, for slow Gaussian noise, the noise always enhances the survival probability ${Q}_{\text{DK}}^{\text{noisy}}$ , due to the absorption of noise quanta across the energy gap. This study not only complements the existing research on the noisy Landau-Zener model but also provides valuable insights into the control of two-level quantum systems.The Demkov-Kunike (DK) model, characterized by a time-dependent Rabi coupling $J\phantom{\rule{0.16em}{0ex}}\text{sech}(t/T)$ and on-site detuning ${\mathrm{\ensuremath{\Delta}}}_{0}+{\mathrm{\ensuremath{\Delta}}}_{1}tanh(t/T)$, has one of the most general forms of an exactly solvable two-state quantum system and therefore it provides a paradigm for coherent manipulations of a qubit's quantum state. Despite its extensive application in noise-free cases, the exploration of the noisy DK model remains limited. Here we extend the coherent DK model to take into account a noisy coupling term $J\ensuremath{\rightarrow}{J}_{\text{noisy}}(t)$. We consider colored Markovian noise sources represented by telegraph noise and Gaussian noise. We present exact solutions for the survival probability ${Q}_{\text{DK}}^{\text{noisy}}$ of the noisy DK model, namely, the probability of the system to remain in its initial state. For slow telegraph noise, we identify parameter regimes where the survival probability ${Q}_{\text{DK}}^{\text{noisy}}$ is suppressed rather than enhanced by noise. In contrast, for slow Gaussian noise, the noise always enhances the survival probability ${Q}_{\text{DK}}^{\text{noisy}}$, due to the absorption of noise quanta across the energy gap. This study not only complements the existing research on the noisy Landau-Zener model but also provides valuable insights into the control of two-level quantum systems.

arXiv:2309.06448Physical Review AFeb 16, 20244 citations

Asymmetric Version of the Second Demkov–Kunike Level-Crossing Model

Artur Mikhailovich Ishkhanyan, T. A. Shahverdyan, A. M. Ghazaryan

Abstract We present a novel time-dependent two-state model that describes a constant-amplitude level-crossing field configuration, where the frequency detuning varies within a finite interval. A distinctive feature of this configuration is that the resonance crossing always occurs asymmetrically in time, making it an asymmetric version of the second Demkov-Kunike model. The general solution of the problem is expressed in terms of two independent irreducible linear combinations of the Gauss hypergeometric functions. We analyze the asymptotes of the solution in terms of corresponding quasi-energies and calculate the final transition probability in the case when the system starts from the first quasi-energy state.Abstract We present a novel time-dependent two-state model that describes a constant-amplitude level-crossing field configuration, where the frequency detuning varies within a finite interval. A distinctive feature of this configuration is that the resonance crossing always occurs asymmetrically in time, making it an asymmetric version of the second Demkov-Kunike model. The general solution of the problem is expressed in terms of two independent irreducible linear combinations of the Gauss hypergeometric functions. We analyze the asymptotes of the solution in terms of corresponding quasi-energies and calculate the final transition probability in the case when the system starts from the first quasi-energy state.

Optical Memory and Neural NetworksDec 1, 20234 citations

An alternative order parameter for the 4-state potts model

Henrique A. Fernandes, Everaldo Arashiro, J. R. Drugowich de Felício +1 more

arXiv:cond-mat/0509066Physica A Statistical Mechanics and its ApplicationsMar 21, 200617 citations

Demkov-Kunike models with decay

M. B. Kenmoe, A. B. Tchapda, Lukong Cornelius Fai

Exact analytical solutions to the dissipative time-dependent Schrödinger equation are obtained for a decaying two-state system with decay rates Γ1 and Γ2 for the levels with extremal spin projections. The system is coherently driven with a pulse whose detuning is made up of two parts: a time-dependent part (chirp) of hyperbolic-tangent shape and a static part with real and imaginary terms. This gives us a wide range of possibilities to arbitrarily select the interaction terms. We considered two versions which led to decaying Demkov-Kunike (DK) models; the version in which the Rabi frequency (interaction) is a time-dependent hyperbolic-secant function (called decaying DK1 model) and the case when it is constant in time and never turns off (decaying DK2 model). Our analytical solutions account for all possible initial moments instead of only t0 = 0 or t0 = − ∞ as for non-decaying models and may be useful for the experiments on level crossings. Two complementary limits of the pulse detuning are considered and explored: the limit of fast (i) and slow rise (ii). In the case (i), the coupling between level positions in the first DK model collapses, while the second DK model reduces to a Rabi model (constant Hamiltonian), in the case (ii), both DK models reduce to the LZ model. In both cases (i) and (ii), analytical approximated solutions which conveniently approach the exact solutions are derived.Exact analytical solutions to the dissipative time-dependent Schrödinger equation are obtained for a decaying two-state system with decay rates Γ1 and Γ2 for the levels with extremal spin projections. The system is coherently driven with a pulse whose detuning is made up of two parts: a time-dependent part (chirp) of hyperbolic-tangent shape and a static part with real and imaginary terms. This gives us a wide range of possibilities to arbitrarily select the interaction terms. We considered two versions which led to decaying Demkov-Kunike (DK) models; the version in which the Rabi frequency (interaction) is a time-dependent hyperbolic-secant function (called decaying DK1 model) and the case when it is constant in time and never turns off (decaying DK2 model). Our analytical solutions account for all possible initial moments instead of only t0 = 0 or t0 = − ∞ as for non-decaying models and may be useful for the experiments on level crossings. Two complementary limits of the pulse detuning are considered and explored: the limit of fast (i) and slow rise (ii). In the case (i), the coupling between level positions in the first DK model collapses, while the second DK model reduces to a Rabi model (constant Hamiltonian), in the case (ii), both DK models reduce to the LZ model. In both cases (i) and (ii), analytical approximated solutions which conveniently approach the exact solutions are derived.

arXiv:1307.3878Journal of Mathematical PhysicsDec 1, 20167 citations

Investigations of Some Four-Field Parametric Interactions

B. P. Kirsanov

Springer eBooksJan 1, 19730 citations

The Demkov-Kunike (DK) model, characterized by a time-dependent Rabi coupling

J\phantom{\rule{0.16em}{0ex}}\text{sech}(t/T)

and on-site detuning ${\mathrm{\ensuremath{\Delta}}}_{0}+{\mathrm{\ensuremath{\Delta}}}_{1}tanh(t/T)$, has one of the most general forms of an exactly solvable two-state quantum system and therefore it provides a paradigm for coherent manipulations of a qubit's quantum state. Despite its extensive application in noise-free cases, the exploration of the noisy DK model remains limited. Here we extend the coherent DK model to take into account a noisy coupling term $J\ensuremath{\rightarrow}{J}_{\text{noisy}}(t)$. We consider colored Markovian noise sources represented by telegraph noise and Gaussian noise. We present exact solutions for the survival probability

{Q}_{\text{DK}}^{\text{noisy}}

of the noisy DK model, namely, the probability of the system to remain in its initial state. For slow telegraph noise, we identify parameter regimes where the survival probability

{Q}_{\text{DK}}^{\text{noisy}}

is suppressed rather than enhanced by noise. In contrast, for slow Gaussian noise, the noise always enhances the survival probability

{Q}_{\text{DK}}^{\text{noisy}}

, due to the absorption of noise quanta across the energy gap. This study not only complements the existing research on the noisy Landau-Zener model but also provides valuable insights into the control of two-level quantum systems.