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Physical Review A

Stabilization of adiabatic population transfer by strong coupling to a phonon bath

Michael Werther, Frank Großmann

Published Dec 11, 2020• 11 citations
Publisher

Abstract

We investigate the influence of the environment on the rapid adiabatic passage scheme for optimal population transfer in a two-level system. To cope with strong coupling to an external phonon bath with super-Ohmic spectral density, we are solving the time-dependent Schr\"odinger equation of the extended system, including a finite number of bath modes using the multi-Davydov D2 ansatz. This allows for the treatment of the non-Markovian reduced dynamics of the two-level subsystem. Surprisingly, it is found that strong system-bath coupling stabilizes the transition probability from the lower to the upper level as a function of the area under the laser pulse. This dissipative engineering effect could only be uncovered by a non-Markovian treatment. For strong coupling, the transition probability then becomes a monotonically increasing function of the pulse area at zero temperature of the heat bath. Finite temperatures break the monotonicity in the range of pulse areas that we studied, but not the stability of the observed effect.

DOI
10.1103/physreva.102.063710

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We investigate the influence of the environment on the rapid adiabatic passage scheme for optimal population transfer in a two-level system. To cope with strong coupling to an external phonon bath with super-Ohmic spectral density, we are solving the time-dependent Schr"odinger equation of the extended system, including a finite number of bath modes using the multi-Davydov D2 ansatz. This allows for the treatment of the non-Markovian reduced dynamics of the two-level subsystem. Surprisingly, it is found that strong system-bath coupling stabilizes the transition probability from the lower to the upper level as a function of the area under the laser pulse. This dissipative engineering effect could only be uncovered by a non-Markovian treatment. For strong coupling, the transition probability then becomes a monotonically increasing function of the pulse area at zero temperature of the heat bath. Finite temperatures break the monotonicity in the range of pulse areas that we studied, but not the stability of the observed effect.
This work investigates the effect of phonon coupling on the transfer of population and creation of coherence using variant of stimulated Raman adiabatic passage (STIRAP) known as \emph{fractional} stimulated Raman adiabatic passage (FSTIRAP). The study is based on the Liouville equation, which is solved numerically in the adiabatic limit. Although the phonon is assumed to be coupled only to the intermediate state, it is coupled to the other two states by dipolar system-environment interaction, inducing phonon coupling to the other states which are not directly in contact with the phonon. At zero temperature the STIRAP pulse protocol's efficiency of the transfer decreases exponentially with the electron-phonon coupling, until the coupling strength is strong enough to make the process fully incoherent, in which case the population transfer is 13\frac{1}{3}31​ in each level. For the FSTIRAP protocol we find that the transferred population to target state decreases, leaving some population on the intermediate state. Consequently, there is an increase in the magnitude of the coherences ρ01,ρ12ρ_{01}, ρ_{12}ρ01​,ρ12​, albeit small. Furthermore population transfer for non-zero temperature and effect of coupling strength is investigated, it is observed that while both parameters negatively influence the efficiency of transfer the former decrease the transfer exponentially, thereby equilibrating the system fast, while the latter seen to decrease the transfer monotonically, and hence equilibrates slowly.
Understanding heat transfer between a quantum system and its environment is of grave importance if reliable quantum devices are to be constructed. Here, the heat transfer between the system and bath in non-Markovian open quantum systems in the process of adiabatic speedup is investigated. Using the quantum state diffusion equation method, the heat current, energy current and the power are calculated during the free evolution and under external control of the system. While the heat current increases with increasing system-bath coupling strength and bath temperature, the non-Markovian nature of the bath can restrict the heat current. Without pulse control, the heat current is nearly equal to energy current. However, with pulse control, the energy current is nearly equal to the power. We show that more non-Markovian baths can be used to better approximate an adiabatic evolution and have a smaller heat current. Our results reveal that the non-Markovian nature of the bath significantly contributes to both the heat transfer rate as well as the effective adiabatic speedup.
Abstract Adiabatic evolution has important applications in quantum information processing. In that context, the system has to be maintained in one of its instantaneous eigenstates. Normally the adiabaticity of the system will be ruined by its surrounding environment. Quantum control has been used widely to speed up the adiabatic process and thus reduces the effect of the environment. In this letter, we investigate the adiabatic speedup and the associated quantum heat current with and without pulse control. The system is immersed in a non-Markovian and finite-temperature heat bath. Our calculation results show that the effective adiabatic speedup can be obtained in a weak system-bath coupling and low-temperature heat bath. Specifically, non-Markovianity from the environment can be beneficial to the enhancement of the adiabatic fidelity. Furthermore, we calculate the quantum heat current between the system and bath in the process of adiabatic speedup. We find that the adiabatic fidelity decreases with increasing heat current. Our investigation paves the way for the design of quantum heat engines and quantum devices.
The interaction of a pair of copropagating pulses with three-level \ensuremath{\Lambda}-type atoms is discussed in terms of time-dependent coupled and decoupled superpositions \ensuremath{\Vert}\ifmmode\pm\else\textpm\fi{}〉 of the lower levels. Due to the explicit time dependence of these states there is a nonadiabatic coupling between the ``bright'' state \ensuremath{\Vert}+〉 and the ``dark'' state \ensuremath{\Vert}-〉 in addition to the strong coupling between \ensuremath{\Vert}+〉 and the upper level \ensuremath{\Vert}a〉 . We show that under quasiadiabatic conditions and in the presence of decay from the upper level this coupling can be treated perturbatively and the Maxwell-Bloch equations can be solved analytically. With the help of such a perturbation approach, coherent population transfer and formstable laser pulse propagation are studied. \textcopyright{} 1996 The American Physical Society.
Population transfer via chirped rapid adiabatic passage is studied using open quantum and semiclassical models, with and without the rotating-wave approximation. A time-dependent variational approach based on the multiple-Davydov D2_22​ trial state is employed to simulate the quantum models with an arbitrary finite mean photon number. We examine the accuracy of both the semiclassical field description and the rotating-wave approximation. Robust population transfer is identified over a wide parameter regime controlled by the laser spectral chirp and is found to be insensitive to the spin--phonon coupling strength, Gaussian pulse area, and energy gap of the two-level system.
The quantum dynamics of the dissipative two-level system with nonzero bias and sub-Ohmic bath is studied by means of the perturbation approach based on a unitary transformation. It has been shown that for the sub-Ohmic bath it is necessary to use the non-Markovian approach, especially for the short time behavior of the coupled system and environment. The nonequilibrium correlation P(t)P(t)P(t) has been calculated to show that a finite bias may favor the short time coherence. The spectrum of the susceptibility ${\ensuremath{\chi}}^{\ensuremath{''}}(\ensuremath{\omega})$ of the sub-Ohmic case may have a double peak structure in the range of $\ensuremath{\omega}>0$ when the coupling $\ensuremath{\alpha}$ is relatively strong. Besides, the coherence-decoherence transition point ${\ensuremath{\alpha}}_{c}$ is determined for different $0<s\ensuremath{\le}1$ by the condition of ${\ensuremath{\chi}}^{\ensuremath{''}}(\ensuremath{\omega}=0)=\ensuremath{\infty}$ when $\ensuremath{\alpha}={\ensuremath{\alpha}}_{c}$. Finally, we show that Shiba's relation is exactly satisfied in our results.