In this thesis, we discuss the possibilities for suppression of decoherence, the loss of purity in an open quantum system, and the related process of dephasing. In the first chapter, we review the literature on the subject of open system dynamics, decoherence and methods of decoherence suppression. In the second chapter, we focus on the specific case of a rotationally hot diatomic molecule as an example of an open quantum system, where molecular vibrational wavepackets are subject to dephasing due to rovibrational coupling. We report analytical and numerical results addressing whether the dephasing rate can be controlled by adjustment of the initial wavepacket phases. It appears that over long timescales, phase-only control is not possible, but for earlier timescales the possibility of phase-only control of dephasing remains. In addition, we point out that the time-dependence of the dephasing process depends significantly upon the degeneracy of the rotational environment states. In the final chapter, we discuss the same system, but apply a qualitatively different method of dephasing suppression based on the nonlinear resonance effect in a driving field. We extend previous work on the topic (Shapiro et al. [1]) by considering the effect of using a train of laser pulses as the driving field, in place of a two-colour continuous-wave laser field. We demonstrate that the pulse train method can be more effective at suppressing dephasing than the two-colour CW case.
In this thesis, we discuss the possibilities for suppression of decoherence, the loss of purity in an open quantum system, and the related process of dephasing. In the first chapter, we review the literature on the subject of open system dynamics, decoherence and methods of decoherence suppression. In the second chapter, we focus on the specific case of a rotationally hot diatomic molecule as an example of an open quantum system, where molecular vibrational wavepackets are subject to dephasing due to rovibrational coupling. We report analytical and numerical results addressing whether the dephasing rate can be controlled by adjustment of the initial wavepacket phases. It appears that over long timescales, phase-only control is not possible, but for earlier timescales the possibility of phase-only control of dephasing remains. In addition, we point out that the time-dependence of the dephasing process depends significantly upon the degeneracy of the rotational environment states. In the final chapter, we discuss the same system, but apply a qualitatively different method of dephasing suppression based on the nonlinear resonance effect in a driving field. We extend previous work on the topic (Shapiro et al. [1]) by considering the effect of using a train of laser pulses as the driving field, in place of a two-colour continuous-wave laser field. We demonstrate that the pulse train method can be more effective at suppressing dephasing than the two-colour CW case.
We consider a rotationally hot diatomic molecule as an example of an open quantum system, where molecular vibrational wave packets are subject to dephasing due to rovibrational coupling. We report analytical and numerical results addressing whether the dephasing rate can be controlled by adjustment of the initial wave packet phases. It appears that over long time scales, phase-only control is not possible, but for earlier time scales the possibility of phase-only control of dephasing remains. In addition, we point out that the time dependence of the dephasing process depends significantly upon the degeneracy of the rotational environment states.
Any real system, no matter how well isolated, unavoidably interacts with the environment. This interaction makes the evolution of a quantum system nonunitary and destroys the coherence of quantum superpositions. This process, known as decoherence, is widely regarded as the most important and fundamental obstacle to the practical realization of quantum information processing. On the other hand, the objectives of quantum control are predicated on the ability to manipulate the system coherently over a period of time. Quantum control has been applied successfully to several experimental systems and coupling such a controlled system to an environment makes the study of coherence loss possible. The standard model of decoherence is formulated in terms of a system, defined by the observables that can be measured, and a reservoir, de¯ned by those degrees of freedom that are not accessed by observation. The vibrational and rotational degree of freedom of diatomic molecules form an experimental model of such a system and bath 1. The nature of the ro-vibrational coupling does not allow a Decoherence Free Subspace, instead we try to identify a Decoherence Resistant Subspace using closed loop control. We set up a learning control loop experiment to monitor the coherence in a vibrational wavepacket, consisting of about 6 vibrational states of the A(1Σ+g ) electronic state, excited by a shaped, ultrashort optical pulse, and then to determine the pulse shape that yielded the longest coherence lifetime. The coherence of the vibrational wavepacket was monitored by measuring the fluorescence quantum beats from the outer turning point of the wave packet's trajectory. The closed loop controller altered the shape of the driving optical pulse to maximize the the depth of modulation of the quantum beats at a prescribed time after excitation, within the constraints of the laser system. The outcome of this closed loop control experiment shows an improvement of the beat decay constant of about 60%, as shown in Fig. (1), a result which occurs for several di®erent pulse shapes. Our experiments show that a number of interesting decoherence-resistant excitations exist. The nature of the dephasing was examined theoretically. Using measured optical pulse shapes, we simulated numerically the molecular wavepacket in the limit of perturbation theory. The experiment and simulations show that there are di®erent mechanisms contributing to the decoherence resistant excitation. The shaped pulse reduces the °uctuations in the wave packet spatial extent, which in turn changes the system reservoir coupling. Other components of the optimal pulse are a sequence of pulses that creates constructive interference of the vibrational wavepacket at the desired time, and chirp which compensates for the anharmonicity of the adiabatic potential. The experimental results show general agreement with numerical simulations. We conclude that wavepackets resistant to dephasing do exist,and that learning algorithms provide an effcient means for finding them.
In the first part of this thesis, we investigate the dynamics of open quantum systems coupled in a purely dephasing way to their environment, which is a paradigmatic example of decoherent dynamics. We focus more specifically on the emergence of non-Markovian effects in the dynamics of such open systems. After reviewing different measures of non-Markovianity, we obtain an analytical expression for the reduced density operator of a finite-dimensional open system coupled with its environment through time-dependent purely dephasing interactions. When the system is initially uncorrelated with its environment, we obtain the time-local master equation that describes its dynamics. In this case, we also derive an exact expression for the witness of non-Markovianity based on the volume of accessible states of the open system. These results are then applied to spin systems coupled to either a spin or a bosonic environment. For spin environments, we study non-Markovianity for different ranges of interaction and in different thermodynamical limits. Moreover, the generation of entanglement between the open system and its environment as well as between spins within the open system is investigated. For bosonic environments, we study the effect of the initial state of the environment on non-Markovianity. We also show that time-dependent modulations of the system-environment coupling can dramatically alter the non-Markovian behavior of the open system. Finally, we consider the case of an open quantum system simultaneously coupled to spin and bosonic baths. In that case, we study how the coupling between the different baths and of the presence of initial correlations in the environment affect the non-Markovianity displayed by the open quantum system. The second part of this thesis is a contribution to the investigation of how quantum systems can be used to process information. More precisely, we focus on the implementation of gate-based quantum computing using neutral atoms trapped in optical or magnetic lattices and interacting through dipole-dipole interactions when excited to Rydberg states. In this context, we present protocols implementing two-qubit quantum gates between atoms far apart in the lattice. To this end, we propose to use a chain of non-coding ancilla atoms to transfer the state of the control qubit to an atom near the target qubit. Before discussing entangling gates between distant qubits, we present two protocols that implement state transfer along a chain of two-level atoms relying respectively on single- and two-atom laser pulses combined with dipole blockade. After reviewing protocols implementing CZ and CNOT gates between nearby qubits using dipole-dipole interactions, we show how the state-transfer protocols previously presented can be used to perform entangling gates between distant qubits. The performance of the state-transfer and gate protocols are assessed using the process fidelity. Moreover, we provide a theoretical explanation for the behavior of the process fidelity with respect to dissipation and imperfect blockade.
Quantum mechanics has both deepened our understanding of the physical reality and allowed development of quantum technologies beating their classical counterparts in efficiency, security, and sensitivity. As a major downside, the quantum properties behind these technologies are very sensitive to the effects the system’s interaction with its environment. The theory of open quantum systems describes how such interaction influences the system, and as a consequence, how the quantum features are lost, controlled, and possibly returned by manipulating the environment. This thesis begins with a short description of the most relevant features and results of the open quantum system theory. We continue by presenting some commonly used measures to quantify the information encoded in quantum systems and the correlations between spatially or temporally separated parties. The literature review ends with discussion of non-Markovianity and memory effects which combine the fields of open quantum systems and quantum information in a natural way. The rest of the thesis presents the main results of Publications I – VII. We study the memory effects and physicality conditions of open system dynamics described by the vast family of phase-covariant master equations. We show how the open quantum system picture can be exploited to design probing protocols to extract information without knowing how the probe and system interact. Such protocols are considered also from the point-of view of efficiently obtaining the information required in the probing, both in theory and by experimental implementation. The experiment serves also as evidence for applicability of recently developed geometric tools to design informationally incomplete measurements for solving so-called membership problems. We present and experimentally realize a protocol where control over intial correlations between polarization and frequency gives full freedom to implement any dephasing dynamics in the open system polarization, thus dictating how its information content changes in time. We study the two-qubit memory effects of dephasing dynamics and compare them to the effect of such noise in the transmission efficiency in superdense coding. Optimal noise configurations in different situations are found. Finally, we characterize the families of initial states for which the decay of quantum correlations depends or does not depend on the noise location.
Next, quantum-classical correspondence in intrinsic decoherence dynamics is examined via purities and reduced density matrices in both the position and energy representations. Dependence of the correspondence on the nature of the coupling potentials and on the initial conditions are discussed. Decoherence effects on quantum and classical dynamics in reactive scattering problems are investigated. Through the study of dynamics of the isotopic analogues of the collinear H + H2 reaction and transmission over simple one-dimensional barrier potentials, the role of decoherence in improving quantum-classical correspondence is identified with suppressing resonance and tunnelling. Finally, the efficiency of 1+3 photon phase control in the presence of decoherence effects phase is carefully examined in several model cases which include from a population inversion in a two-level bound system to IBr photodissociation. Further, the ways to overcome the control loss caused by dephasing are discussed.
The impediment towards the successful development of the field of quantum information (QI) is decoherence , i.e., the loss of entanglement by the effect of the environment on the systems of interest. An important challenge is that of QI engineering, by entanglement and decoherence control, in complex systems, such as unimolecular and bimolecular systems, that can simultaneously handle large amounts of QI. Progress towards this goal can be achieved by: (a) decay modification and decoherence suppression in molecules, using laser-induced phase and amplitude modulation of rovibrational levels and inter-mode couplings; (b) transfer of internal-translational entanglement and teleportation of wavepackets via molecular dissociation and collisions.