Open Quantum System Approach Research Articles

Bottomonium suppression and flow in heavy-ion collisions

The strong suppression of bottomonia production in ultra-relativistic heavy-ion collisions is a smoking gun for the creation of a deconfined quarkgluon plasma (QGP). In this proceedings contribution, I review recent work that aims to provide a more comprehensive and systematic understanding of bottomonium dynamics in the QGP through the use of pNRQCD and an open quantum systems approach. This approach allows one to evolve the heavyquarkonium reduced density matrix, taking into account non-unitary effective Hamiltonian evolution of the wave-function and quantum jumps between different angular momentum and color states. In the case of a strong coupled QGP in which Ebind ≪ T, mD ≪ 1=a0, the corresponding evolution equation is Markovian and can therefore be mapped to a Lindblad evolution equation. To solve the resulting Lindblad equation, we make use of a stochastic unraveling called the quantum trajectories algorithm and couple the non-abelian quantum evolution to a realistic 3+1D viscous hydrodynamical background. Using a large number of Monte-Carlo sampled bottomonium trajectories, we make predictions for bottomonium RAA and elliptic flow as a function of centrality and transverse momentum and compare to data collected by the ALICE, ATLAS, and CMS collaborations.

Non-equilibrium evolution of quarkonium in medium in the open quantum system approach

In this proceedings contribution, I review recent work that aims to provide a more comprehensive and systematic understanding of bottomonium dynamics in the quark-gluon plasma using an open quantum system (OQS) approach that is applied in the framework of the potential non-relativistic QCD (pNRQCD) effective field theory and coupled to realistic hydrodynamical backgrounds that have been tuned to soft hadron observables. I review how the computation of bottomonium suppression can be reduced to solving a Gorini- Kossakowski-Sudarshan-Lindblad (GKSL) equation for the evolution of the bb̅ reduced density matrix, which includes both singlet and octet states plus medium-induced transitions between them at next-to-leading order (NLO) in the binding energy over temperature. Finally, I present comparisons of phenomenological predictions of the NLO OQS+pNRQCD approach and experimental data for bottomonium suppression and elliptic flow in LHC 5.02 TeV Pb-Pb collisions obtained using both smooth and fluctuating hydrodynamic initial conditions.

Nonequilibrium evolution of quarkonium in medium

We review recent progress in open quantum system approach to the description of quarkonium in the quark-gluon plasma. A particular emphasis is put on the Lindblad equations for quarkonium and its numerical simulations.

Probing Kondo spin fluctuations with scanning tunneling microscopy and electron spin resonance

We theoretically analyze a state-of-the-art experimental method based on a combination of electron spin resonance and scanning tunneling microscopy (ESR-STM), to directly probe the spin fluctuations in the Kondo effect. The Kondo impurity is exchange coupled to the probe spin, and the ESR-STM setup detects the small level shifts in the probe spin induced by the spin fluctuations of the Kondo impurity. We use the open quantum system approach by regarding the probe spin as the "system" and the Kondo impurity spin as the fluctuating "bath" to evaluate the resonance line shifts in terms of the dynamic spin susceptibility of the Kondo impurity. We consider various common adatoms on surfaces as possible probe spins and estimate the corresponding level shifts. It is found that the sensitivity is most pronounced for the probe spins with transverse magnetic anisotropy.

Non-reciprocal population dynamics in a quantum trimer.

We study a quantum trimer of coupled two-level systems beyond the single-excitation sector, where the coherent coupling constants are ornamented by a complex phase. Accounting for losses and gain in an open quantum systems approach, we show how the mean populations of the states in the system crucially depend on the accumulated phase in the trimer. Namely, for non-trivial accumulated phases, the population dynamics and the steady states display remarkable non-reciprocal behaviour in both the singly and doubly excited manifolds. Furthermore, while the directionality of the resultant chiral current is primarily determined by the accumulated phase in the loop, the sign of the flow may also change depending on the coupling strength and the amount of gain in the system. This directionality paves the way for experimental studies of chiral currents at the nanoscale, where the phases of the complex hopping parameters are modulated by magnetic or synthetic magnetic fields.

Non-Markovian open quantum system approach to the early Universe: Damping of gravitational waves by matter

By revising the application of the open quantum system approach to the early universe and extending it to the conditions beyond the Markovian approximation, we obtain a new non-Markovian quantum Boltzmann equation. Throughout the paper, we also develop an extension of the quantum Boltzmann equation to describe the processes that are irreversible at the macroscopic level. This new kinetic equation is, in principle, applicable to a wide variety of processes in the early universe. For instance, using this equation one can accurately study the microscopic influence of a cosmic environment on a system of cosmic background photons or stochastic gravitational waves. In this paper, we apply the non-Markovian quantum Boltzmann equation to study the damping of gravitational waves propagating in a medium consisting of decoupled ultra-relativistic neutrinos. For such a system, we study the time evolution of the intensity and the polarization of the gravitational waves. It is shown that, in contrast to intensity and linear polarization which are damped, the circular polarization (V-mode) of the gravitational wave (if present) is amplified by propagating through such a medium.

Open quantum systems for quarkonia

I review recent applications of the open quantum system framework in the understanding of quarkonium suppression in heavy-ion collisions, which has been used as a probe of the quark–gluon plasma for decades. The derivation of the Lindblad equations for quarkonium in both the quantum Brownian motion and the quantum optical limits and their semiclassical counterparts is explained. The hierarchy of time scales assumed in the derivation is justified from the separation of energy scales in nonrelativistic effective field theories of QCD. Physical implications of the open quantum system approach are also discussed. Finally, I list some open questions for future studies.

Tailoring Bose-Einstein-condensate environments for a Rydberg impurity

Experiments have demonstrated that the excitation of atoms embedded in a Bose-Einstein condensate to Rydberg states is accompanied by phonon creation. Here we provide the theoretical basis for the description of phonon-induced decoherence of the superposition of two different Rydberg states. To this end, we determine Rydberg-phonon coupling coefficients using a combination of analytical and numerical techniques. From these coefficients, we calculate bath correlation functions, spectral densities, and reorganization energies. These quantities characterize the influence of the environment and form essential inputs for followup open quantum system approaches. We find that the amplitude of bath correlations scales like the power law ${\ensuremath{\nu}}^{\ensuremath{-}6}$ with the principal quantum number $\ensuremath{\nu}$, while reorganization energies scale exponentially, reflecting the extreme tunability of Rydberg atomic properties.

Theory of microwave-optical conversion using rare-earth-ion dopants

We develop a theoretical description of a device for coherent conversion of microwave to optical photons. For the device, dopant ions in a crystal are used as three-level systems, and interact with the fields inside overlapping microwave and optical cavities. We develop a model for the cavity fields interacting with an ensemble of ions, and model the ions using an open quantum systems approach, while accounting for the effect of inhomogeneous broadening. Numerical methods are developed to allow us to accurately simulate the device. We also further develop a simplified model, applicable in the case of small cavity fields which is relevant to quantum information applications. This simplified model is used to predict the maximum conversion efficiency of the device. We investigate the effect of various parameters, and predict that conversion efficiency of above 80% should be possible with currently existing experimental setups inside a dilution refrigerator.

Chiral Current Circulation and PT Symmetry in a Trimer of Oscillators

We present a simple quantum theory of a bosonic trimer in a triangular configuration, subject to gain and loss in an open quantum systems approach. Importantly, the coupling constants between each oscillator are augmented by complex arguments, which give rise to various asymmetries. In particular, one may tune the complex phases to induce chiral currents, including the special case of completely unidirectional (or one-way) circulation when certain conditions are met regarding the coherent and incoherent couplings. When our general theory is recast into a specific non-Hermitian Hamiltonian, we find interesting features in the trimer population dynamics close to the exceptional points between phases of broken and unbroken $\mathcal{PT}$ symmetry. Our theoretical work provides perspectives for the experimental realization of chiral transport at the nanoscale in a variety of accessible nanophotonic and nanoplasmonic systems, and paves the way for the potential actualization of nonreciprocal devices.

Molecule-photon interactions in phononic environments

Molecules constitute compact hybrid quantum optical systems that can interface photons, electronic degrees of freedom, localized mechanical vibrations and phonons. In particular, the strong vibronic interaction between electrons and nuclear motion in a molecule resembles the optomechanical radiation pressure Hamiltonian. While molecular vibrations are often in the ground state even at elevated temperatures, one still needs to get a handle on decoherence channels associated with phonons before an efficient quantum optical network based on opto-vibrational interactions in solid-state molecular systems could be realized. As a step towards a better understanding of decoherence in phononic environments, we take here an open quantum system approach to the non-equilibrium dynamics of guest molecules embedded in a crystal, identifying regimes of Markovian versus non-Markovian vibrational relaxation. A stochastic treatment based on quantum Langevin equations predicts collective vibron-vibron dynamics that resembles processes of sub- and superradiance for radiative transitions. This in turn leads to the possibility of decoupling intramolecular vibrations from the phononic bath, allowing for enhanced coherence times of collective vibrations. For molecular polaritonics in strongly confined geometries, we also show that the imprint of opto-vibrational couplings onto the emerging output field results in effective polariton cross-talk rates for finite bath occupancies.

Plasmons in two-dimensional lattices of near-field coupled nanoparticles

We consider plasmonic metasurfaces constituted by an arbitrary periodic arrangement of spherical metallic nanoparticles. Each nanoparticle supports three degenerate dipolar localized surface plasmon (LSP) resonances. In the regime where the interparticle distance is much smaller than the optical or near-infrared wavelength associated with the LSPs, the latter couple through the dipole-dipole interaction and form collective plasmonic modes which extend over the whole metasurface. Within a Hamiltonian model which we solve exactly, we derive general expressions which enable us to extract analytically the quasistatic plasmonic dispersion for collective modes polarized within the plane and perpendicular to the plane of the metasurface. Importantly, our approach allows us not only to consider arbitrary Bravais lattices, but also non-Bravais two-dimensional metacrystals featuring nontrivial topological properties, such as, e.g., the honeycomb or Lieb lattices. Additionally, using an open quantum system approach, we consider perturbatively the coupling of the collective plasmons to both photonic and particle-hole environments, which lead, respectively, to radiative and nonradiative frequency shifts and damping rates, for which we provide closed-form expressions. The radiative frequency shift, when added to the quasistatic dispersion relation, provides an approximate analytical description of the fully retarded band structure of the collective plasmons. While it is tempting to make a direct analogy between the various systems which we consider and their electronic tight-binding equivalents, we critically examine how the long-range retarded and anisotropic nature of the dipole-dipole interaction may quantitatively and qualitatively modify the underlying band structures and discuss their experimental observability.

Environment-Assisted and Environment-Hampered Efficiency at Maximum Power in a Molecular Photocell

The molecular photo cell, i.e., a single molecule donor-acceptor complex, beside being technologically important, is a paradigmatic example of a many-body system operating in strong non-equilibrium. The quantum transport and the photo-voltaic energy conversion efficiency of the photocell, attached to two external leads, are investigated within the open quantum system approach by solving the Lindblad master equation. The interplay of the vibrational degrees of freedom corresponding to the molecules (via the electron-phonon interaction) and the environment (via dephasing) shows its signature in the efficiency at maximum power. We find vibration assisted electron transport in the medium to strong electron-phonon coupling regime when the system does not suffer dephasing. Exposure to dephasing hampers such a vibration assisted electron transport in a specific range of dephasing rate.

Quantum Brownian motion of a heavy quark pair in the quark-gluon plasma

In this paper we study the real-time evolution of heavy quarkonium in the quark-gluon plasma (QGP) on the basis of the open quantum systems approach. In particular, we shed light on how quantum dissipation affects the dynamics of the relative motion of the quarkonium state over time. To this end we present a novel non-equilibrium master equation for the relative motion of quarkonium in a medium, starting from Lindblad operators derived systematically from quantum field theory. In order to implement the corresponding dynamics, we deploy the well established quantum state diffusion method. In turn we reveal how the full quantum evolution can be cast in the form of a stochastic non-linear Schr\"odinger equation. This for the first time provides a direct link from quantum chromodynamics (QCD) to phenomenological models based on non-linear Schr\"odinger equations. Proof of principle simulations in one-dimension show that dissipative effects indeed allow the relative motion of the constituent quarks in a quarkonium at rest to thermalize. Dissipation turns out to be relevant already at early times well within the QGP lifetime in relativistic heavy ion collisions.

Optimal efficiency of the Q-cycle mechanism around physiological temperatures from an open quantum systems approach

The Q-cycle mechanism entering the electron and proton transport chain in oxygenic photosynthesis is an example of how biological processes can be efficiently investigated with elementary microscopic models. Here we address the problem of energy transport across the cellular membrane from an open quantum system theoretical perspective. We model the cytochrome {b}_{6},f protein complex under cyclic electron flow conditions starting from a simplified kinetic model, which is hereby revisited in terms of a Markovian quantum master equation formulation and spin-boson Hamiltonian treatment. We apply this model to theoretically demonstrate an optimal thermodynamic efficiency of the Q-cycle around ambient and physiologically relevant temperature conditions. Furthermore, we determine the quantum yield of this complex biochemical process after setting the electrochemical potentials to values well established in the literature. The present work suggests that the theory of quantum open systems can successfully push forward our theoretical understanding of complex biological systems working close to the quantum/classical boundary.

A new approach for open quantum systems based on a phonon number representation of a harmonic oscillator bath

To investigate a system coupled to a harmonic oscillator bath, we propose a new approach based on a phonon number representation of the bath. Compared to the method of the hierarchical equations of motion, the new approach is computationally much less expensive in a sense that a reduced density matrix is obtained by calculating the time evolution of vectors, instead of matrices, which enables one to deal with large dimensional systems. As a benchmark test, we consider a quantum damped harmonic oscillator, and show that the exact results can be well reproduced. In addition to the reduced density matrix, our approach also provides a link to the total wave function by introducing new boson operators.

Generalized open quantum system approach for the electron paramagnetic resonance of magnetic atoms

A recent experimental breakthrough has enabled probing the electronic parametric resonance of a single magnetic atom in a scanning tunneling microscopy setup. The results present intriguing features, such as an asymmetric line shape and an unusually large ratio of the decoherence and decay rates, which defy standard approaches using the conventional Bloch equations. To address these issues we employ generalized Bloch equations, together with proper microscopic modeling of the magnetic adatom, and show how all the experimental features can be naturally accounted for. The proposed approach may also be useful in treating any future similar experiments, as well as next generation hybrid quantum devices.

Ground-state cooling enabled by critical coupling and dark entangled states

We analyze the cooling of a mechanical resonator coupled to an ensemble of interacting two-level systems via an open quantum systems approach. Using an exact analytical result, we find optimal cooling occurs when the phonon mode is critically coupled $(\ensuremath{\gamma}\ensuremath{\sim}g)$ to the two-level system ensemble. Typical systems operate in suboptimal cooling regimes due to the intrinsic parameter mismatch $(\ensuremath{\gamma}\ensuremath{\gg}g)$ between the dissipative decay rate $\ensuremath{\gamma}$ and the coupling factor $g$. To overcome this obstacle, we show that carefully engineering the coupling parameters through the strain profile of the mechanical resonator allows phonon cooling to proceed through the dark (subradiant) entangled states of an interacting ensemble, thereby resulting in optimal phonon cooling. Our results provide an avenue for ground-state cooling and should be accessible for experimental demonstrations.

Room temperature quantum coherence vs. electron transfer in a rhodanine derivative chromophore.

Understanding electron transfer in organic molecules is of great interest in quantum materials for light harvesting, energy conversion and integration of molecules into solar cells. This, however, poses the challenge of designing specific optimal molecular structure for which the processes of ultrafast quantum coherence and electron transport are not so well understood. In this work, we investigate subpicosecond time scale quantum dynamics and electron transfer in an efficient electron acceptor rhodanine chromophoric complex. We consider an open quantum system approach to model the complex-solvent interaction, and compute the crossover from weak to strong dissipation on the reduced system dynamics for both a polar (methanol) and a non polar solvent (toluene). We show that the electron transfer rates are enhanced in the strong chromophore-solvent coupling regime, being the highest transfer rates those found at room temperature. Even though the computed dynamics are highly non-Markovian, and they may exhibit a quantum character up to hundreds of femtoseconds, we show that quantum coherence does not necessarily optimise the electron transfer in the chromophore.

An open quantum system approach to the radical pair mechanism

The development of the radical pair mechanism has allowed for theoretical explanation of the fact that magnetic fields are observed to have an effect on chemical reactions. The mechanism describes how an external magnetic field can alter chemical yields by interacting with the spin state of a pair of radicals. In the field of quantum biology, there has been some interest in the application of the mechanism to biological systems. This paper takes an open quantum systems approach to a model of the radical pair mechanism in order to derive a master equation in the Born-Markov approximation for the case of two electrons, each interacting with an environment of nuclear spins as well as the external magnetic field, then placed in a dissipative bosonic bath. This model is used to investigate two different cases relating to radical pair dynamics. The first uses a collective coupling approach to simplify calculations for larger numbers of nuclei interacting with the radical pair. The second looks at the effects of different hyperfine configurations of the radical pair model, for instance the case in which one of the electrons interact with two nuclei with different hyperfine coupling constants. The results of these investigations are analysed to see if they offer any insights into the biological application of the radical pair mechanism in avian magnetoreception.