A long-lived coherent state and non-linear interaction have been experimentally demonstrated for the vibrational mode of a trapped ion. We propose an implementation of quantum computation using coherent states of the vibrational modes of trapped ions. Differently from earlier experiments, we consider a far-off resonance for the interaction between external fields and the ion in a bidimensional trap. By appropriate choices of the detunings between the external fields, the adiabatic elimination of the ionic excited level from the Hamiltonian of the system allows for beam splitting between orthogonal vibrational modes, production of coherent states and non-linear interactions of various kinds. In particular, this model enables the generation of the four coherent Bell states. Furthermore, all the necessary operations for quantum computation such as preparation of qubits, one-qubit and controlled two-qubit operations, are possible. The detection of the state of a vibrational mode in a Bell state is made possible by the combination of resonant and off-resonant interactions between the ion and some external fields. We show that our read-out scheme provides highly efficient discrimination between all the four Bell states. We extend this to a quantum register composed of many individually trapped ions. In this case, operations on two remote qubits are possible through a cavity mode. We emphasize that our remote-qubit operation scheme does not require a high quality factor resonator: the cavity field acts as a catalyst for the gate operation.
We report an experimental and theoretical study of the evolution of vibrational coherence in a thermal ensemble of nitrogen molecules. Rotational dephasing and rephasing of the vibrational coherence is detected by coherent anti-Stokes Raman scattering. The existence of ro-vibrational coupling and the discrete energy spectrum of the rotational bath lead to a whole new class of full and fractional ro-vibrational revivals. Following the rich ro-vibrational dynamics on a nanosecond time scale with sub-picosecond time resolution enables us to determine the second-order ro-vibrational constant $gamm…
We improve a previously proposed scheme (Phys. Rev. A 66 (2002) 065401) for generating vibrational trio coherent states of a trapped ion. The improved version is shown to gain a double advantage: (i) it uses only five, instead of eight, lasers and (ii) the generation process can be made remarkably faster.
We propose a scheme for preparation of entangled coherent states for the motion of an ion in a two-dimensional anisotropic trap. In the scheme, the ion is driven by four laser beams along different directions in the ion trap plane, resulting in carrier excitation and couplings between the internal and external degrees of freedom. When the total quantum number of the vibrational modes initially has a definite parity, the competition between the unitary dynamics and spontaneous emission will force the system to evolve to a steady state, where the vibrational modes are in a two-mode cat state. We…
Recent experiments [K. R. Brown, et al., Nature 471, 196 (2011); and M. Harlander, et al., Nature 471, 200 (2011)] have demonstrated the coherent manipulations on the external vibrations of two ions, confined individually in the separated ion traps. Using these recently developed techniques, we propose here an approach to realize the coherent operations, e.g., the universal quantum gates, between the separated ion-trap qubits encoded by two internal atomic states of the trapped ions. Our proposal operates beyond the usual Lamb-Dicke limits, and could be applied to the scalable ion traps couple…
Multi-dimensional spectroscopy represents a particularly insightful tool for investigating the interplay of nuclear and electronic dynamics, which plays an important role in a number of photophysical processes and photochemical reactions. Here we present a coherent state representation of the vibronic dynamics and of the resulting response functions for the widely used linearly displaced oscillator model. Analytical expressions are initially derived for the case of third-order response functions in an N-level system, with ground state initialization of the oscillator (zero-temperature limit). …
A coherent control scheme for the population distribution in the vibrational states of nonpolar molecules is proposed. Our theoretical analysis and results of numerical simulations for the interaction of the hydrogen molecular ion in its electronic ground state with an infrared laser pulse reveal a selective two-photon transition between the vibrational states via a coupling with the first excited dissociative state. We demonstrate that for a given temporal intensity profile the population transfer between vibrational states, or a superposition of vibrational states, can be made complete for a…
We show how entangled qubits can be encoded as entangled coherent states of two-dimensional centre-of-mass vibrational motion for two ions in an ion trap. The entangled qubit state is equivalent to the canonical Bell state, and we introduce a proposal for entanglement transfer from the two vibrational modes to the electronic states of the two ions in order for the Bell state to be detected by resonance fluorescence shelving methods.
We demonstrate coherent control of population transfer between vibrational states in an optical lattice by using interference between a one-phonon transition at $2ω$ and a two-phonon transition at $ω$. The $ω$ and $2ω$ transitions are driven by phase- and amplitude-modulation of the lattice laser beams, respectively. By varying the relative phase between these two pathways, we control the branching ratio of transitions to the first excited state and to the higher states. Our best result shows an improvement of the branching ratio by a factor of 3.5$\pm$0.7. Such quantum control techniques may …
We propose a scheme for generating vibrational pair coherent states of the motion of an ion in a two-dimensional trap. In our scheme, the trapped ion is excited bichromatically by three laser beams along different directions in the X-Y plane of the ion trap. We show that if the initial vibrational state is given by a two-mode Fock state, the final steady state, indicated by the extinction of the fluorescence emitted by the ion, is a pure state. The motional state of the ion in the equilibrium realizes that of the highly-correlated pair coherent state.
Recent evidence suggests that quantum effects may have functional importance in biological light-harvesting systems. Along with delocalized electronic excitations, it is now suspected that quantum coherent interactions with certain near-resonant vibrations may contribute to light-harvesting performance. However, the actual quantum advantage offered by such coherent vibrational interactions has not yet been established. We investigate a quantum design principle, whereby coherent exchange of single energy quanta between electronic and vibrational degrees of freedom can enhance a light-harvesting…
Coherent control of bound state processes via the interfering overlapping resonances scenario [Christopher et al., J. Chem. Phys. 123, 064313 (2006)] is developed to control intramolecular vibrational redistribution (IVR). The approach is applied to the flow of population between bonds in a model of chaotic OCS vibrational dynamics, showing the ability to significantly alter the extent and rate of IVR by varying quantum interference contributions.
Giant strides in ultrashort laser pulse technology have enabled real-time observation of dynamical processes in complex molecular systems. Specifically, the discovery of oscillatory transients in the two-dimensional electronic spectra of photosynthetic systems stimulated a number of theoretical investigations exploring possible physical mechanisms of the remarkable quantum efficiency of light harvesting processes. However, the theories employed have reached a high degree of sophistication and have become complex, making it difficult to gain insights into microscopic processes and biologically …
We propose a scheme to generate superpositions of coherent states for the vibrational motion of a laser cooled trapped-ion. It is based on the interaction with a standing wave making use of the counter-rotating terms, i.e. not applying the rotating wave approximation. We also show that the same scheme can be exploited for quantum state measurement, i.e. with the same scheme non-classical states may be reconstructed
A pair of coherent femtosecond pulse excitations applied to a molecule with strong electron-phonon coupling creates a coherent superposition of a low momentum and a high momentum wavepacket in the vibrational states of both the excited state and the ground state of the coherent transition. As the excited state is accelerated further, interference between the high momentum ground state contribution and the low momentum excited state contribution causes a photon echo. This photon echo is a direct consequence of quantum interference between separate vibrational trajectories and can therefore prov…
A new physical implementation for quantum computation is proposed. The vibrational modes of molecules are used to encode qubit systems. Global quantum logic gates are realized using shaped femtosecond laser pulses which are calculated applying optimal control theory. The scaling of the system is favourable, sources for decoherence can be eliminated. A complete set of one and two quantum gates is presented for a specific molecule. Detailed analysis regarding experimental realization shows that the structural resolution of today's pulse shapers is easiliy sufficient for pulse formation.
We propose a scheme for measuring the Berry phase in the vibrational degree of freedom of a trapped ion. Starting from the ion in a vibrational coherent state we show how to reverse the sign of the coherent state amplitude by using a purely geometric phase. This can then be detected through the internal degrees of freedom of the ion. Our method can be applied to preparation of Schrödinger cat states.
The interplay between an open quantum system and its environment can lead to both coherent and incoherent behaviour. We explore the extent to which strong coupling to a single bosonic mode can alter the coherence properties of a two-level system in a structured environment. This mode is treated exactly, with the rest of the environment comprising a Markovian bath of bosonic modes. The strength of the coupling between the two-level system and the single mode is varied for a variety of different forms for the bath spectral density in order to assess whether the coherent dynamics of the two-level…
A chirped-pulse quantum control scheme applicable to Coherent Anti-Stokes Raman Scattering spectroscopy, named as C-CARS, is presented aimed at maximizing the vibrational coherence in molecules. It implies chirping of three incoming pulses in the four-wave mixing process of CARS, the pump, the Stokes and the probe, to fulfil the conditions of adiabatic passage. The scheme is derived in the framework of rotating wave approximation and adiabatic elimination of excited state manifold simplifying the four-level model system into a ``super-effective'' two level system. The robustness, spectral sele…
Optical spectroscopy with broadband femtosecond laser pulses often involves simultaneous excitation of multiple molecular species with close resonance frequencies. Interpreting the collective optical response from molecular mixtures typically requires Fourier analysis of the detected time-resolved signal. We propose an alternative method of separating coherent optical responses from two molecular species with neighboring excitation resonances (here, vibrational modes of oxygen and carbon dioxide). We utilize ro-vibrational coupling as a mechanism of suppressing the strong vibrational response …
We propose an ideal scheme for preparing vibrational $\mathrm{SU(1,1)} \otimes \mathrm{SU(1,1)}$ states in a two-dimensional ion trap using red and blue second sideband resolved driving of two orthogonal vibrational modes. Symmetric and asymmetric driving provide two regimes to realize quantum state engineering of the vibrational modes. In one regime, we show that time evolution synthesizes so-called $\mathrm{SU}(1,1)$ Perelomov coherent states, that is separable squeezed states and their superposition too. The other regime allows engineering of lossless 50/50 $\mathrm{SU}(2)$ beam splitter st…
We demonstrate a strong coherent backward wave oscillation using forward propagating fields only. This is achieved by applying laser fields to an ultra-dispersive medium with proper chosen detunings to excite a molecular vibrational coherence that corresponds to a backward propagating wave. The physics then has much in common with propagation of ultra-slow light. Applications to coherent scattering and remote sensing are discussed.
The roles of the vibration motions played in the excitation energy transfer process are studied. It is found that a strong coherent transfer in the hybrid system emerges when the detuning between the donor and the acceptor equals the intrinsic frequency of the vibrational mode, and as a result the energy can be transferred into the acceptor much effectively. Three cases of the donor and the acceptor coupling with vibrational modes are investigated respectively. We find that the quantum interference between the two different transfer channels via the vibrational modes can affects the dynamics o…
In this paper, we extend a method recently reported [Phys. Rev. E 87, 042921 (2012)] for the calculation of the eigestates of classically highly chaotic systems to cases of mixed dynamics, i.e. those presenting regular and irregular motions at the same energy. The efficiency of the method, which is based on the use of a semiclassical basis set of localized wave functions, is demonstrated by applying it to the determination of the vibrational states of a realistic molecular system, namely the LiCN molecule.
We study the quantum dynamics of an ultracold atomic gas in a deep optical lattice within an optical high-$Q$ resonator. The atoms are coherently illuminated with the cavity resonance tuned to a blue vibrational sideband, so that photon scattering to the resonator mode is accompanied by vibrational cooling of the atoms. This system exhibits a threshold above which pairwise stimulated generation of a cavity photon and an atom in the lowest vibrational band dominates spontaneous scattering and we find a combination of optical lasing with a buildup of a macroscopic population in the lowest lattic…
We consider the quantum processor based on a chain of trapped ions to propose an architecture wherein the motional degrees of freedom of trapped ions (position and momentum) could be exploited as the computational Hilbert space. We adopt a continuous-variables approach to develop a toolbox of quantum operations to manipulate one or two vibrational modes at a time. Together with the intrinsic non-linearity of the qubit degree of freedom, employed to mediate the interaction between modes, arbitrary manipulation and readout of the ionic wave function could be achieved.
We introduce a generalized class of states called K-quantum nonlinear coherent states. Each K-state has K j-components corresponding to one and the same eigenvalue. Each Kj-component can be composed of K K=1-states in a correlated manner. The introduced states are shown to be realized in the long-term behavior of the vibrational motion of an ion properly trapped and laser-driven. Nonclassical properties of the states are studied in detail.
The optical hybridization of the electronic states in strongly coupled molecule-cavity systems have revealed unique properties such as lasing, room temperature polariton condensation, and the modification of excited electronic landscapes involved in molecular isomerization. Here we show that molecular vibrational modes of the electronic ground state can also be coherently coupled with a micro-cavity mode at room temperature, given the low vibrational thermal occupation factors associated with molecular vibrations, and the collective coupling of a large ensemble of molecules immersed within the…
Epiphenomenalism is shown to be absurd because the development of consciousness must be explainable through natural selection. A detailed neuromolecular basis of the neuromediator release is given and it is stressed on the possible key point where the quantum mind could act, namely presynaptic scaffold protein dynamics and detachment of the calcium sensor v-SNARE synaptotagmin-1. The beta-neurexin molecules are tuned via fast propagating solitons by the quantum coherent microtubule network so that the beta-neurexin molecule thermal vibrations could promote or suppress conformational changes vi…
We propose an implementation of quantum logic gates via virtual vibrational excitations in an ion trap quantum computer. Transition paths involving unpopulated, vibrational states interfere destructively to eliminate the dependence of rates and revolution frequencies on vibrational quantum numbers. As a consequence quantum computation becomes feasible with ions whos vibrations are strongly coupled to a thermal reservoir.
We study the quantum dynamics of diatomic molecule driven by a circularly polarized resonant electric field. We look for a quantum effect due to classical chaos appearing due to the overlapping of nonlinear resonances associated to the vibrational and rotational motion. We solve the Schrödinger equation associated with the wave function expanded in term of proper stationary states, $|n>\otimes|lm>$ (vibrational$\otimes$angular momentum states). Looking for quantum-classic correspondence, we consider the Liouville dynamics in the two dimensional phase space defined by the coherent -like state o…
Curvilinear kinetic energy models are developed for variational nuclear motion computations including the inter- and the low-frequency intra-molecular degrees of freedom of the formic acid dimer. The coupling of the inter- and intra-molecular modes is studied by solving the vibrational Schrödinger equation for a series of vibrational models, from two up to ten active vibrational degrees of freedom by selecting various combinations of active modes and constrained coordinate values. Vibrational states, nodal assignment, and infrared vibrational intensity information is computed using the the ful…
We present the computation of two-photon transition spectra between ro-vibrational states of the H2+ molecular ion, including the effects of hyperfine structure and excitation polarization. The reduced two-photon matrix elements are obtained by means of a variational method. We discuss the implications of our results for high-resolution spectroscopy of H2+.
Atomic lattice clocks have spurred numerous ideas for tests of fundamental physics, detection of general relativistic effects, and studies of interacting many-body systems. On the other hand, molecular structure and dynamics offer rich energy scales that are at the heart of new protocols in precision measurement and quantum information science. Here we demonstrate a fundamentally distinct type of lattice clock that is based on vibrations in diatomic molecules, and present coherent Rabi oscillations between weakly and deeply bound molecules that persist for 10's of milliseconds. This control is…
Vibrational degrees of freedom in trapped-ion systems have recently been gaining attention as a quantum resource, beyond the role as a mediator for entangling quantum operations on internal degrees of freedom, because of the large available Hilbert space. The vibrational modes can be represented as quantum harmonic oscillators and thus offer a Hilbert space with infinite dimension. Here we review recent theoretical and experimental progress in the coherent manipulation of the vibrational modes, including bosonic encoding schemes in quantum information, reliable and efficient measurement techni…
In this paper we design and use two Deep Learning models to generate the ground and excited wavefunctions of different Hamiltonians suitable for the study the vibrations of molecular systems. The generated neural networks are trained with Hamiltonians that have analytical solutions, and ask the network to generalize these solutions to more complex Hamiltonian functions. This approach allows to reproduce the excited vibrational wavefunctions of different molecular potentials. All methodologies used here are data-driven, therefore they do not assume any information about the underlying physical …
Experimental and theoretical evidence point out to the crucial role of specific resonant intramolecular vibrational modes in the interpretation of long-lived coherences observed in two-dimensional spectra of some natural and synthetic light harvesting complexes. For the natural situation of illumination by incoherent (sun)light, the relevance of these vibrations is analyzed here for light-harvesting vibronic prototype dimers. The detailed analysis of the density matrix dynamics reveals that the inclusion of the intramolecular vibrational modes reinforce up to one order of magnitude the exciton…
Dipole-coupled subwavelength quantum emitter arrays respond cooperatively to external light fields as they may host collective delocalized excitations (a form of excitons) with super- or subradiant character. Deeply subwavelength separations typically occur in molecular ensembles, where in addition to photon-electron interactions, electron-vibron couplings and vibrational relaxation processes play an important role. We provide analytical and numerical results on the modification of super- and subradiance in molecular rings of dipoles including excitations of the vibrational degrees of freedom.…
Methodological progress is reported in the challenging direction of a black-box-type variational solution of the (ro)vibrational Schrödinger equation applicable to floppy, polyatomic systems with multiple large-amplitude motions. This progress is achieved through the combination of (i) the numerical kinetic-energy operator (KEO) approach of [E. Mátyus, G. Czakó, and A. G. Császár, J. Chem. Phys. 130, 134112 (2009)] and (ii) the Smolyak non-product grid method of [G. Avila and T. Carrington, Jr., J. Chem. Phys. 131, 174103 (2009)]. The numerical representation of the KEO makes it possible to ch…
We characterize both entanglement and quantum coherence in a molecular system by connecting the linear entropy of electronic-nuclear entanglement with Wigner-Yanase skew information measuring vibronic coherence and local quantum uncertainty on electronic energy. Linear entropy of entanglement and quantifiers of quantum coherence are derived for a molecular system described in a bipartite Hilbert space H=Hel x Hvib of finite dimension Nel x Nv, and relations between them are established. For the specific case of the electronic-vibrational entanglement, we find the linear entropy of entanglement…
We simulate the long-range inter-complex electronic energy transfer in Photosystem II -- from the antenna complex, via a core complex, to the reaction center -- using a non-Markovian (ZOFE) quantum master equation description that allows us to quantify the electronic coherence involved in the energy transfer. We identify the pathways of the energy transfer in the network of coupled chromophores, using a description based on excitation probability currents. We investigate how the energy transfer depends on the initial excitation -- localized, coherent initial excitation versus delocalized, inco…
The electromagnetic field in an optical cavity can dramatically modify and even control chemical reactivity via vibrational strong coupling (VSC). Since the typical vibration and cavity frequencies are considerably higher than thermal energy, it is essential to adopt a quantum description of cavity-catalyzed adiabatic chemical reactions. Using quantum transition state theory (TST), we examine the coherent nature of adiabatic reactions and derive the cavity-induced changes in eigen frequencies, zero-point-energy, and quantum tunneling. The resulting quantum TST calculation allows us to explain …
The present discussion rises a number of the questions. For example, is rotational coherence of large molecules necessarily destroyed in the conventionally statistical limit of structureless non-selective continuum (for fixed total spin and parity values) under the conditions of complete intramolecular energy redistribution and vibrational dephasing in the regime of strong ro-vibrational coupling? For the slow cross-symmetry phase relaxation, quantum coherent superpositions of a large number of complex configurations with, e.g., many different total angular momenta produce image of a rotation …
We control the quantum mechanical motion of neutral atoms in an optical lattice by driving microwave transitions between spin states whose trapping potentials are spatially offset. Control of this offset with nanometer precision allows for adjustment of the coupling strength between different motional states, analogous to an adjustable effective Lamb-Dicke factor. This is used both for efficient one-dimensional sideband cooling of individual atoms to a vibrational ground state population of 97%, and to drive coherent Rabi oscillation between arbitrary pairs of vibrational states. We further sh…
We discuss Floquet engineering of dissipative molecular systems through periodic driving of an infrared-active vibrational transition, either directly or via a cavity mode. Following a polaron quantum Langevin equations approach, we derive correlation functions and stationary quantities showing strongly modified optical response of the infrared-dressed molecule. The coherent excitation of molecular vibrational modes, in combination with the modulation of electronic degrees of freedom due to vibronic coupling can lead to both enhanced vibronic coherence as well as control over vibrational sideb…
