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.

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 wavepacket͒ 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 Schrödinger 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.

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 realization of these goals. Here we show how strongly correlated states of ultracold atoms can be detected 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 it to detect various standard and "exotic" types of antiferromagnetic order in lattice systems and by indicating the feasibility of detection of superfluid order in Fermi liquids.Introduction Future applications of quantum physics for quantum simulations, computation, communication, and metrology will require an extremely high degree of control of preparation, manipulation, and, last but not least, detection of strongly correlated states of quantum many body systems. Ultracold atoms offer an unprecedented playground for realization of these goals. Several paradigm examples of strongly correlated states have been successfully realized, such as the Mott insulator, the Tonks gas, and the Bose glass (for a review cf. [1]). A standard way of analyzing such systems is by releasing the atoms from the trap and performing destructive absorption spectroscopy, which only allows to measure the column density of the expanded cloud. Considerable attention has been thus devoted recently to novel methods of detection, that allow for measuring (spin) densitydensity and other higher order correlation functions. One of those methods is atomic noise interferometry [2], whose power is well illustrated in the recent observation of the bosonic and the fermionic Hanbury Brown-Twiss effect [3,4]. Direct atom counting is another way to measure this effect, and to even go beyond it [5]; it can be realized directly with metastable Helium atoms [6,7], or by using methods of cavity quantum electrodynamics (QED) [8]. Cavity QED is also essential in the recent proposals of Ref. [9,10], while Ref. [11] proposes how to prepare and detect magnetic quantum phases using superlattices. All of the above approaches are, at least in some respects, destructive and frequently suffer from undesired atom number fluctuations inevitable in the preparation of the quantum states.

Recent experimental observations of time-dependent beatings in the two-dimensional echo-spectra of light-harvesting complexes at ambient temperatures have opened up the question of whether coherence and wave-like behaviour play a significant role in photosynthesis. We carry out a numerical study of the absorption and echo-spectra of the Fenna-Matthews-Olson (FMO) complex in Chlorobium tepidum and analyse the requirements in the theoretical model needed to reproduce beatings in the calculated spectra. The energy transfer in the FMO pigment-protein complex is theoretically described by an exciton Hamiltonian coupled to a phonon bath which accounts for the pigments' electronic and vibrational excitations, respectively. We use the hierarchical equations of motions method to treat the strong couplings in a non-perturbative way. We show that the oscillations in the two-dimensional echo-spectra persist in the presence of thermal noise and static disorder. 3 different information from the population dynamics and needs to be calculated and analysed separately in detail. In principle, techniques such as quantum state and process tomography made out of a sequence of 2D echo-spectra can be used to map out the complete density matrix [13]. In contrast to energy-transfer efficiency studies where an initial excitation enters the complex at specific sites close to the antenna, in 2D echo-spectra the whole complex is simultaneously excited. Also the two-exciton manifold yields prominent contributions to the signal, resulting in negative regions in the 2D echo-spectra.The non-pertubative calculation of 2D echo-spectra presents a considerable computational challenge owing to the presence of two excitons giving rise to excited state absorption and the requirement to consider ensemble averages over differently orientated complexes with slightly varying energy levels. Previous calculations have used Markovian approximations [14,15] or exclude the double-exciton manifold [16]. In addition, the systematic study of beatings in a series of 2D echo-spectra requires an effective means of calculating a huge number of such spectra. So far, no theoretical method has been able to describe the long-lasting beatings in the time-resolved 2D spectra [14,16,17]. One possible explanation for the persistence of long coherence times has been the sluggish absorption of the reorganization energy by the molecule, which requires theoretical descriptions that go beyond the Markovian approximation and the rotating wave approximation [18]. The hierarchical equations of motions (HEOM), first developed by Tanimura and Kubo [19] and subsequently refined in [20][21][22][23], show oscillations in the dynamics of the exciton populations that persist even at temperature T = 300 K [24,25]. The HEOM include the reorganization process in a transparent way and are directly applicable to computations at physiological temperatures. A calculation at temperature 77 K of the 2D echospectra with the HEOM method has recently been performed by Chen et al [17], which does not di...

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