System Bath Research Articles

Creation of entanglement by interaction with a common heat bath.

I show that entanglement between two qubits can be generated if the two qubits interact with a common heat bath in thermal equilibrium, but do not interact directly with each other. In most situations the entanglement is created for a very short time after the interaction with the heat bath is switched on, but depending on system, coupling, and heat bath, the entanglement may persist for arbitrarily long times. This mechanism sheds new light on the creation of entanglement. A particular example of two quantum dots in a closed cavity is discussed, where the heat bath is given by the blackbody radiation.

Investigation of ONO‐AE1‐259, A Selective Prostanoid EP 2 ‐Receptor Agonist, on the Guinea‐Pig Isolated Saphenous Vein

There are no selective agonists for the prostanoid EP4-receptor, and the ones available for the EP2-receptor are either of low potency (e.g. AH 13205) or are C1-methyl esters subject to variable de-esterification within tissues (e.g. butaprost). EP4 vasorelaxant systems are often highly sensitive, with IC50 values for PGE2 as low as 0.1 nM, whereas EP2 systems are usually some 30–100 times less sensitive. Determining whether EP2-receptors co-exist with EP4-receptors is therefore quite difficult. Some information can be gained using the EP4 antagonist AH 23848, but this blocker has a low affinity (pA2= 5.0–5.4), making large dose ratios difficult to obtain. We have recently investigated the utility of a new EP2 agonist, ONO-AE1-259 in this situation. ONO-AE1-259 (free acid) is claimed to be highly selective on the basis of radioligand competition and second messenger measurements on cloned mouse receptors; its EC50 for cyclic AMP production = 1.8 nM for EP2 and >10 μM for EP4-receptors (S. Narumiya; 11th International Conference on Prostaglandins, Florence, 2000). Rings of guinea-pig lateral saphenous vein were set up in a 4-channel Mulvaney myograph system (bath volume = 5 ml) in Krebs-Henseleit solution containing 1 μM indomethacin and 0.2 μM GR 32191 (TP antagonist). Tone was generated with 3 μM phenylephrine and agonists were added cumulatively. PGE2 induced ∼95% relaxation at 5 nM and had an EC50 of about 0.1 nM. ONO-AE1-259 consistently showed small relaxant effects at 1 nM, but its log concentration-response curve was shallower than that of PGE2 and only about 85% relaxation was found at 5 μM (IC50= 20 nM relative to its own maximum). The vein preparation did not contact to sulprostone, and therefore is unlikely to contain opposing EP1 and/or EP3 systems. In the presence of 30 μM AH 23848, the log concentration-response curve for PGE2 was displaced to the right in a parallel manner (dose ratio = 7.6, pA2= 5.3). However, the ONO-AE1-259 curve was only slightly displaced to the right by AH 23848 (dose ratio = 1.6), while at the same time maximum relaxation was reduced by 15%. ONO-AE1-259 was about 25 times more potent than butaprost. It is possible therefore that ONO-AE1-259 is selectively activating a relaxant EP2-receptor in the guinea-pig saphenous vein. The saphenous vein preparation is also highly sensitive to the prostacyclin analogues AFP-07 (IC50= 0.65 nM) and cicaprost (IC50= 7 nM). We are investigating whether these analogues activate IP and/or EP4 receptors, in the light of our recent finding that they are potent and moderately potent EP4 agonists respectively on both piglet and rabbit saphenous veins (Jones & Chan, 2001, Br. J. Pharmacol., in press).

The validity of quantum–classical multi-channel diffusion equations describinginterlevel transitions in the condensed phase. The adiabatic representation

We develop an approach for derivation of quantum–classical relaxation equationsfor a two-channel problem. The treatment is based on the adiabatic channelwavefunctions and the system–bath coupling is modelled as a bilinearinteraction in momentum representation. In the quantum–classical limit weobtain Liouville equations with the relaxation operator containing diffusionterms diagonal in Liouvillian space and the off-diagonal part which isresponsible for thermal interlevel transitions. The high-frequency interlevelquantum beats are fully taken into account in this relaxation term. Inthe framework of the present formulation and as a consequence of themomentum-dependent interaction the Smoluchovsky diffusion limit can bereached without invoking Fokker–Planck equations as an intermediate step. Theinherent property of equations so obtained is that the partial rates ofinterlevel transitions obey the principle of detailed balance. This result couldnot be gained in earlier treatments of the two-level diffusion problem.

Vibrational spectroscopy of a harmonic oscillator system nonlinearly coupled to a heat bath

Vibrational relaxation of a harmonic oscillator nonlinearly coupled to a heat bath is investigated by the Gaussian–Markovian quantum Fokker–Planck equation approach. The system–bath interaction is assumed to be linear in the bath coordinate, but linear plus square in the system coordinate modeling the elastic and inelastic relaxation mechanisms. Interplay of the two relaxation processes induced by the linear–linear and square–linear interactions in Raman or infrared spectra is discussed for various system–bath couplings, temperatures, and correlation times for the bath fluctuations. The one-quantum coherence state created through the interaction with the pump laser pulse relaxes through different pathways in accordance with the mechanisms of the system–bath interactions. Relations between the present theory, Redfield theory, and stochastic theory are also discussed.

Theory of open quantum systems

A quantum dissipation theory is constructed with the system–bath interaction being treated rigorously at the second-order cumulant level for both reduced dynamics and initial canonical boundary condition. The theory is valid for arbitrary bath correlation functions and time-dependent external driving fields, and satisfies correlated detailed-balance relation at any temperatures. The general formulation assumes a particularly simple form in driven Brownian oscillator systems in which the correlated driving-dissipation effects can be accounted for exactly in terms of local-field correction. Remarks on a class of widely used phenomenological quantum master equations that neglects the bath dispersion-induced dissipation are also made in contact with the present theory.

A model of spontaneous generation of population inversion in open quantum systems

Mathematical theorems by Davies justify, upon a specific choice of the scaling parameter, the weak-coupling relaxation theory. We use this exact mathematics again but with another, equally admissible and physically motivated, scaling parameter beyond regime of the weak system–bath coupling. This allows us to study very specific particle vs. surroundings correlations of a type known from, e.g., molecular biology. A model utilizing these correlations is suggested and solved using the above rigorous mathematics here. It yields successive spontaneous excitation of a particle at positive bath temperatures to finite number of excited states, with even dominating asymptotic population of the highest one, challenging thus standard statistical thermodynamics. Model assumptions are shortly discussed but no approximate steps are involved.

Ultrafast cis-trans photoswitching: A model study

A quantum-mechanical model description of a molecular photoswitch is developed. It takes into account (i) the electronic curve crossing arising from the cis-trans twisting of a double bond, resulting in an ultrafast internal-conversion process of the system and (ii) the coupling of the initially excited chromophore (the “system”) to the remaining degrees of freedom (the “bath”), affecting a vibrational cooling of the hot photoproducts. The latter mechanism is responsible for the localization of the molecule in the cis and trans configuration, respectively, thus determining the quantum yield of the photoreaction. Following a discussion of the validity and the numerical implementation of the Redfield formulation employed, detailed numerical studies of the time-dependent dissipative photoisomerization dynamics are presented. While the short-time dynamics (≲1 ps) is dominated by the coherent wave-packet motion of the system, the time evolution at larger times mainly reflects the interaction between system and bath. The quantum yield of the cis-trans forward reaction (Yc→t) and the trans-cis backward reaction (Yt→c) is shown to depend on the energy storage of the photoreaction and, in particular, on the form of the system–bath coupling. On the other hand, it is found that Yt→c=1−Yc→t, that is the population probabilities of the cis and trans configuration at long times do not depend on the initial preparation of the system.

Dynamics of primary charge separation in bacterial photosynthesis using the multilevel Redfield-Davies secular approach

We use Redfield's relaxation theory in the Davies formulation to study primary charge separation reactions in bacterial photosynthesis. The specific model studied is the standard one (spin-boson), with three states for the system, harmonic oscillators for the bath, and linear ohmic system–bath coupling. The Redfield–Davies formulation, which is equivalent to the secular approximation, is Markovian, of second order in system–bath coupling, and is written for the system's density matrix. The approximation does not suffer from any negative probabilities (which appear in the original Redfield approach) and can therefore be used for long-time processes (20 ps or more here). Our results are in line with previous studies, especially to high bath frequencies. They confirm the usefulness of the Redfield–Davies secular approach as a convenient and simple tool for studying system–bath processes. © 2002 John Wiley & Sons, Inc. Int J Quantum Chem, 2002

Anharmonic effects on photo-induced electron transfer: A Redfield approach

Photo-induced electron transfer experiments examine intrinsically nonequilibrium processes. A theoretical description of photoinduced processes should take into account the fact that the approximations and assumptions made for equilibrium electron transfer need not be appropriate. Under nonequilibrium conditions, anharmonic distortions in the potential energy surfaces of nuclear motion coupled to the electron transfer may effect the dynamics. This work is a study of the effects of anharmonicity on photo-induced electron transfer reactions for condensed phase systems where one vibrational mode is strongly coupled to the electron transfer and a stochastic bath. For this vibrational mode, both harmonic and anharmonic potential energy surfaces for the excited states are considered and the electron transfer dynamics is monitored in a range of system–bath coupling regimes. The study focuses on two effects due to anharmonic distortions of the intramolecular modes: changes to the system Hamiltonian, and differences in the dephasing processes caused by the anharmonic distortions. These calculations show that for small differences in the donor and acceptor state energies, the effects of vibrational anharmonicity is very small. However, when this energy difference is large, the dynamics for anharmonic and harmonic modes is significant. The relative role played by the competing physical processes is easily understood by examining the vibronic state populations obtained using a multistate Redfield approach.

Nonlinear response functions for the three-dimensional spectroscopies

Theoretical descriptions of the three-dimensional spectroscopies are presented in this paper by calculating the associated nonlinear response function. Previously, the harmonic approximation with the Wick’s theorem was used to obtain theoretical expression of the three-dimensional vibrational response function, by treating the mechanical and electrical anharmonicities perturbatively. However, the bath-induced memory effect and anharmonicity-induced frequency shift were not correctly taken into account by the previous theory. By incorporating the system–bath interaction properly, the general nonlinear response functions for the three-dimensional vibrational, vibrational-electronic, or electronic spectroscopies are obtained and discussed in detail. By using the resultant nonlinear response function, two-color vibrational photon echo, three-dimensional sum- and difference-frequency generation spectroscopies, and two-color infrared pump–probe spectroscopy are theoretically proposed.

Effects of temperature on the nonlinear response function for two-dimensional vibrational spectroscopy

We investigate the effects of temperature on the nonlinear response functions associated with various two-dimensional vibrational spectroscopies. It turns out that the system–bath interaction plays an important role in determining the nature of the temperature-dependencies of the nonlinear response functions and spectra of the two-dimensional vibrational spectroscopy. For a model Hamiltonian, we present exact quantum-mechanical expressions for the nonlinear response functions of two-dimensional vibrational spectroscopies in both the time and frequency domains.

Semiclassical description of quantum coherence effects and their quenching: A forward–backward initial value representation study

The forward–backward (FB) version of the semiclassical (SC) initial value representation (IVR) is used to study quantum coherence effects in the time-dependent probability distribution of an anharmonic vibrational coordinate and its quenching when coupled to a thermal bath. It is shown that the FB-IVR accurately reproduces the detailed quantum coherent structure in the weak coupling regime, and also describes how this coherence is quenched with an increase of the system–bath coupling and/or the bath temperature. Comparisons are made with other approximations and the physical implications are discussed.

Random-matrix model for quantum Brownian motion

We use a random band-matrix model for the system–bath interaction to derive a Markovian master equation for the time evolution of one-dimensional quantum systems weakly coupled to a heat bath. We study in detail the damped harmonic oscillator and discuss the fluctuation-dissipation relation. In the large-bandwidth, high-temperature limit, our master equation coincides with the equations derived by Agarwal and Caldeira–Leggett. This shows that the Markovian master equations for quantum Brownian motion are independent of model assumptions used in their derivation and, thus, universal.

Open-system quantum dynamics for gas-surface scattering: Nonlinear dissipation and mapped Fourier grid methods

When a gas phase atom or molecule hits a nonrigid surface, both elastic and inelastic scattering and sticking can occur. We suggest treating the dynamics of these processes using open-system density matrix theory. For the “free→free” and “free→bound” events at hand, both fundamental and numerical problems arise. The fundamental problem is that the adsorbate “system” is anharmonic and the coupling between the system and the substrate “bath” has to be nonlinear at least in the system coordinates. Here we propose a new Lindblad-type open-system density matrix approach which accounts for system anharmonicity and nonlinearity of the system–bath coupling. The numerical problem is that for a dissipative scattering process large basis sets or grids are required, making the storage and direct propagation of a density matrix difficult. To overcome this problem we use a mapped Fourier method which reduces the grid size and hence the storage requirements significantly. We apply the new methods and techniques to a simple model resembling the simultaneous scattering and sticking of an O2 molecule at a metal surface.

Chirped pulse excitation in condensed phases involving intramolecular modes studied by double-sided Feynman diagrams for fast optical dephasing

The effect of the quantum intramolecular modes on the chirped pulse excitation in condensed phase has been studied. Nonperturbative equations for the populations of molecular electronic states under the action of intense chirped pulses have been obtained using the double-sided Feynman diagrams. We have shown that the application of this technique to systems with fast electronic dephasing enables us to include strong system–bath interactions (non-Markovian relaxation) and to perform the summation of diagrams. We have studied the influence of the chirp rate on the integral population of the excited state n2 after the completion of pulse action. We have shown that the effect of the quantum intramolecular modes strongly depends on the carrier pulse frequency. Incorporating these modes increases n2 when a molecule is excited near the 0→1 transition with respect to the quantum intramolecular vibration. If the molecule is excited near the 0→0 transition with respect to the intramolecular mode, the effect is opposite.

Environment-induced corrections to the spin Hamiltonian as dynamic frequency shifts in nuclear magnetic resonance

We derive an expression for the correction to the spin-system Hamiltonian that arises due to the system–bath interaction, starting both from the standard master equation for the spin density matrix and a perturbative diagonalization of the system–bath Hamiltonian to the second order in the interaction. We show that the dynamic frequency shifts observed in the evolution of the nuclear spin coherences are a result of these Hamiltonian corrections. We present a systematic decomposition of the relaxation superoperator into Hermitian and anti-Hermitian parts as opposed to the usual practice of partitioning it into real and imaginary parts. We point out that the relaxation-induced corrections to the coherent motion arise exclusively from the anti-Hermitian part and the dissipative effects, from the Hermitian part, both, in general, being complex. However, the secular terms of this correction are found to depend only on the imaginary and the real parts, respectively.

On the second-order corrections to the quantum canonical equilibrium density matrix

We consider the equilibrium state of a quantum system weakly coupled to a quantum bath within second order perturbation theory. It was previously shown by Romero-Rochin and Oppenheim [Physica A 155, 52 (1989)] that the equilibrium state deviates from the canonical form, e−βHs/Zs (Hs is the free system Hamiltonian and Zs the canonical partition function). We reproduce this result via a different derivation, starting from the non-Markovian, rather than the Markovian, quantum Master equation. Our derivation sheds new light on the mechanism that stabilizes the deviation from the canonical form and shows that it involves an interplay between a static distortion to the equilibrium state and dynamical system–bath correlations. We show that this deviation is a necessary consequence of translational invariance and vanishes when the rotating-wave-approximation is applied. The deviation is also shown to vanish for a two-level system off-diagonally coupled to a heat bath or when the Lamb shifts are neglected. Two ways for numerically evaluating the second order deviations are described. Finally, the deviations from canonical equilibrium are given an illuminating geometrical interpretation in terms of the phase space Wigner distribution.

System–bath coupling dynamics by femtosecond pump–probe spectroscopy

Femtosecond pump–probe spectroscopy of a laser dye IR132 in the solvent DMSO has been performed. It is shown that the experimental spectra generated following excitation at two different wavelengths can be reasonably reproduced by simulations starting from an assumed system–bath energy autocorrelation function. The correlation times and coupling strengths compare favorably with results from previous studies. A novel oscillation of the spectral width is observed in the experimental spectra that can be traced to out of phase oscillations of the vibrational wavepacket between the ground and excited electronic states.

Non-Markovian evolution of the density operator in the presence of strong laser fields

We present an accurate, efficient, and flexible method for propagating spatially distributed density matrices in anharmonic potentials interacting with solvent and strong fields. The method is based on the Nakajima–Zwanzig projection operator formalism with a correlated reference state of the bath that takes memory effects and initial/final correlations to second order in the system–bath interaction into account. A key feature of the method proposed is a special parametrization of the bath spectral density leading to a set of coupled equations for primary and N auxiliary density matrices. These coupled master equations can be solved numerically by representing the density operator in eigenrepresentation or on a coordinate space grid, using the Fourier method to calculate the action of the kinetic and potential energy operators, and a combination of split operator and Cayley implicit method to compute the time evolution. The key advantages of the method are: (1) The system potential may consist of any number of electronic states, either bound or dissociative. (2) The cost for arbitrarily long solvent memories is equal to only N+1 times that of propagating a Markovian density matrix. (3) The method can treat explicitly time-dependent system Hamiltonians nonperturbatively, making the method applicable to strong field spectroscopy, photodissociation, and coherent control in a solvent surrounding. (4) The method is not restricted to special forms of system–bath interactions. Choosing as an illustrative example the asymmetric two-level system, we compare our numerical results with full path-integral results and we show the importance of initial correlations and the effects of strong fields onto the relaxation. Contrary to a Markovian theory, our method incorporates memory effects, correlations in the initial and final state, and effects of strong fields onto the relaxation; and is yet much more effective than path integral calculations. It is thus well-suited to study chemical systems interacting with femtosecond short laser pulses, where the conditions for a Markovian theory are often violated.

Improved power series expansion for the time evolution operator: Application to two-dimensional systems

The power series expansion formalism is used to construct analytical approximations for the propagator of the partial differential equation of a generic type. The present approach is limited to systems with polynomial coefficients. Three typical two-dimensional examples, a Hénon–Heiles anharmonic resonating system, a system–bath Hamiltonian, and a Fokker–Planck chaotic model are considered. All results are in excellent agreement with those of an established numerical scheme in the field. It is found that the power series expansion method accurately describes the dynamics of very anharmonic processes in the whole time domain.