Mirta Rodríguez

Time evolution of pendular states created by the interaction of molecular polarizability with a pulsed nonresonant laser field

Previous investigations have shown that the instantaneous eigenstates of a molecule interacting via its polarizability with a strong electric field of a nonresonant laser pulse are pendular hybrids of field-free rotational states, aligned along the field direction. However, nonadiabatic effects during the time evolution of the initial field-free rotational state could cause the molecule to end up in a state described by a linear combination of pendular states (a rotational wavepacket) whose alignment properties are not a priori known. We report a computational study of the time evolution of these states. We solve the reduced time-dependent Schrodinger equation for an effective Hamiltonian acting within the vibronic ground state. Our numerical results show that the time evolution and the achievement of adiabatic behavior depend critically on the detailed characteristics of the laser pulse and the rotational constant of the molecule.

High-Performance Solution of Hierarchical Equations of Motion for Studying Energy Transfer in Light-Harvesting Complexes

Excitonic models of light-harvesting complexes, where the vibrational degrees of freedom are treated as a bath, are commonly used to describe the motion of the electronic excitation through a molecule. Recent experiments point toward the possibility of memory effects in this process and require one to consider time nonlocal propagation techniques. The hierarchical equations of motion (HEOM) were proposed by Ishizaki and Fleming to describe the site-dependent reorganization dynamics of protein environments ( J. Chem. Phys. 2009 , 130 , 234111 ), which plays a significant role in photosynthetic electronic energy transfer. HEOM are often used as a reference for other approximate methods but have been implemented only for small systems due to their adverse computational scaling with the system size. Here, we show that HEOM are also solvable for larger systems, since the underlying algorithm is ideally suited for the usage of graphics processing units (GPU). The tremendous reduction in computational time due to the GPU allows us to perform a systematic study of the energy-transfer efficiency in the Fenna-Matthews-Olson (FMO) light-harvesting complex at physiological temperature under full consideration of memory effects. We find that approximative methods differ qualitatively and quantitatively from the HEOM results and discuss the importance of finite temperature to achieving high energy-transfer efficiencies.

Quantum non-demolition detection of strongly correlated systems

Preparation, manipulation and detection of strongly correlated states of quantum many-body systems are among the most important goals and challenges of modern physics. Ultracold atoms offer an unprecedented playground for the realization of these goals. Here, we propose a method for detecting strongly correlated states of ultracold atoms in a quantum non-demolition scheme, that is, in the fundamentally least destructive way permitted by quantum mechanics. In our method, spatially resolved components of atomic spins couple to quantum polarization degrees of freedom of light. In this way, quantum correlations of matter are faithfully mapped on those of light; the latter can then be efficiently measured using homodyne detection. We illustrate the power of such spatially resolved quantum-noise-limited polarization measurement by applying this method to the detection of various standard and ‘exotic’ types of antiferromagnetic order in lattice systems, and by indicating the feasibility of detection of superfluid order in Fermi liquids.

Quantum polarization spectroscopy of correlations in attractive fermionic gases

We show how spin–spin correlations, detected in a non-destructive way via spatially resolved quantum polarization spectroscopy, strongly characterize various phases realized in trapped ultracold fermionic atoms. Polarization degrees of freedom of the light couple to spatially resolved components of the atomic spin. In this way, quantum fluctuations of matter are faithfully mapped onto those of light. In particular, we demonstrate that quantum spin polarization spectroscopy provides a direct method to detect the Fulde–Ferrell–Larkin–Ovchinnikov phase realized in a one-dimensional imbalanced Fermi system.

Modeling of Transient Absorption Spectra in Exciton–Charge-Transfer Systems

Time-resolved spectroscopy provides the main tool for analyzing the dynamics of excitonic energy transfer in light-harvesting complexes. Inferring the time scales and effective coupling parameters from experimental data requires the development of numerically exact theoretical models. The finite duration of the laser-molecule interactions and the reorganization process during the exciton migration affect the location and strength of spectroscopic signals. We show that the nonperturbative hierarchical equations of motion method captures these processes in a model exciton system, including the charge-transfer state.

Counting of fermions and spins in strongly correlated systems in and out of thermal equilibrium

Atom counting theory can be used to study the role of thermal noise in quantum phase transitions and to monitor the dynamics of a quantum system. We illustrate this for a strongly correlated fermionic system, which is equivalent to an anisotropic quantum XY chain in a transverse field and can be realized with cold fermionic atoms in an optical lattice. We analyze the counting statistics across the phase diagram in the presence of thermal fluctuations and during its thermalization when the system is coupled to a heat bath. At zero temperature, the quantum phase transition is reflected in the cumulants of the counting distribution. We find that the signatures of the crossover remain visible at low temperature and are obscured with increasing thermal fluctuations. We find that the same quantities may be used to scan the dynamics during the thermalization of the system.

Two-dimensional electronic spectra of the photosynthetic apparatus of green sulfur bacteria

Advances in time resolved spectroscopy have provided new insight into the energy transmission in natural photosynthetic complexes. Novel theoretical tools and models are being developed in order to explain the experimental results. We provide a model calculation for the two-dimensional electronic spectra of Cholorobaculum tepidum which correctly describes the main features and transfer time scales found in recent experiments. From our calculation one can infer the coupling of the antenna chlorosome with the environment and the coupling between the chlorosome and the Fenna-Matthews-Olson complex. We show that environment assisted transport between the subunits is the required mechanism to reproduce the experimental two-dimensional electronic spectra.

Tailored particle current in an optical lattice by a weak time-symmetric harmonic potential

Quantum ratchets exhibit asymptotic currents when driven by a time-periodic potential of zero mean if the proper spatiotemporal symmetries are broken. Recently, there has been debate on whether directed currents may arise for potentials which do not break these symmetries. We show here that in the presence of degeneracies in the quasienergy spectrum, long-lasting directed currents can be induced, even if the time-reversal symmetry is not broken. Our model can be realized with ultracold atoms in optical lattices in the tight-binding regime, and we show that the time scale of the average current can be controlled by extremely weak fields.

Long-lasting molecular alignment: Fact or fiction?

It has been suggested that appropriate periodic sequences of laser pulses can maintain molecular alignment for arbitrarily long times [J. Ortigoso, Phys. Rev. Lett. 93, 073001 (2004)]. These aligned states are found among the cyclic eigenstates of truncated matrix representations of the one-period time propagator U(T,0). However, long time localization of periodic driven systems depends on the nature of the spectrum of their exact propagator; if it is continuous, eigenstates of finite-basis propagators cease to be cyclic, in the long time limit, under the exact time evolution. We show that, for very weak laser intensities, the evolution operator of the system has a point spectrum for most laser frequencies, but for the laser powers needed to create aligned wave packets it is unknown if U(T,0) has a point spectrum or a singular continuous spectrum. For this regime, we obtain error bounds on the exact time evolution of rotational wave packets that allow us to determine that truncated aligned cyclic states do not lose their alignment for millions of rotational periods when they evolve under the action of the exact time propagator.

Particle-counting statistics of time- and space-dependent fields

The counting statistics give insight into the properties of quantum states of light and other quantum states of matter such as ultracold atoms or electrons. The theoretical description of photon counting was derived in the 1960s and was extended to massive particles more recently. Typically, the interaction between each particle and the detector is assumed to be limited to short time intervals, and the probability of counting particles in one interval is independent of the measurements in previous intervals. There has been some effort to describe particle counting as a continuous measurement, where the detector and the field to be counted interact continuously. However, the formalism based on continuous measurements does not provide a formula applicable to general time- and space-dependent fields. In our work, we derive a fully time- and space-dependent description of the counting process for linear quantum many-body systems, taking into account the back-action of the detector on the field. We apply our formalism to an expanding Bose-Einstein condensate of ultracold atoms, and show that it describes the process correctly, whereas the standard approach gives unphysical results in some limits. The example illustrates that, in certain situations, the back-action of the detector cannot be neglected and has to be included in the description.