Session Z33: Open Quantum Systems and Decoherence

Quantum Darwinism in hazy environments

Quantum Darwinism provides an information-theoretic framework for the emergence of the classical world from the quantum substrate. It recognizes that we - the observers - acquire our information about the ``systems of interest'' indirectly from their imprints on the environment. Objectivity, a key property of the classical world, arises via the proliferation of redundant information into the environment where many observers can then intercept it and independently determine the state of the system. After a general introduction to this framework, we demonstrate how non-ideal initial states of the environment (e.g., mixed states) affect its ability to act as a communication channel for information about the system. The environment's capacity for transmitting information is directly related to its ability to increase its entropy. Therefore, environments that remain nearly invariant under the Hamiltonian dynamics, such as very mixed states, have a diminished ability to transmit information. However, despite this, the environment almost always redundantly transmits information about the system.   

Critical dynamics of decoherence

Quantum decoherence is the key to how the classical world emerges from the quantum substrate. Its understanding is also essential for creation of nanoscale devices that need long-time quantum coherence for their operation (e.g., quantum computers). Here we study for the first time how the non-equilibrium quench of the environment affects decoherence of the quantum system. Namely, we investigate decoherence of a central spin-1/2 surrounded by the environment that is driven through a quantum critical point. The quantum Ising model in the transverse field serves as the environment. Thus, we combine extensive studies of decoherence with rapidly growing field of dynamics of quantum phase transitions. We show that coherence of the central spin undergoes rapid decay that encodes critical exponents of the environment as well as exhibits certain periodicities that allow for identification of the central spin -- environment coupling and ground state fidelity. Our discussion is based on a remarkably simple analytical expression verified through numerical simulations.   

Limits of quantum speedup in photosynthetic light harvesting

It has been suggested that excitation transport in photosynthetic light harvesting complexes features speedups analogous to those found in quantum algorithms. Here we compare dynamics in these systems to quantum walks to elucidate the limits of such quantum speedups. For the Fenna-Matthews-Olson (FMO) complex of green sulfur bacteria, we show that while there is indeed speedup at short times, this is short lived (70 fs) despite longer lived (ps) quantum coherence. Remarkably, this time scale is independent of the details of the decoherence model. More generally, we show that the distinguishing features of light-harvesting complexes limit quantum speedup and cause even diffusive transport to be slowed. These results suggest that quantum coherent effects in biological systems are optimized for efficiency and robustness rather than for achieving the more elusive goal of quantum speedup.   

Decoherence and Disentanglement of Two Intereacting Qubits in the Presence of Random Telegraphic Noise

We have studied the dissipative dynamics of a pair of quits coupled via the exchange interaction in the presence of random telegraphic noise. We use a recently developed transfer-matrix formalism that is suitable for computing the temporal evolution of a quantum system affected by a classical stochastic process. For bipartite systems, the concurrence provides a measure of the entanglement between two qubits. We have calculated the concurrence as a function of the qubit working point, noise coupling strength, fluctuator rates and exchange interaction strengths. Sudden death of entanglement and its revival are seen to depend on various factors. We show that for certain cases, the exchange interaction between the qubits can be used to significantly slow down the decoherence process and maintain entanglement over much longer periods of time. This could be particularly promising for quantum computing applications.   

Two-Qubit Disentanglement and Decoherence from Classical Random Telegraph Noise

We consider the two-qubit disentanglement due to classical random telegraph noise where the qubits do not interact and have tunable working points. Using a new mathematical method that is suited to treat all working points, we show that entanglement sudden death and revival are dependent on several factors, such as qubit working point, noise coupling strength and initial state entanglement. For extended Werner states, the concurrence is related to the difference of two functions: one is related to dephasing and the other longitudinal relaxation.~ A physical interpretation based on a generalized Bloch sphere representation is given.   

Resonant regimes in the Fock-space coherence of non-equilibrium quantum dots

We investigate theoretically the real-time evolution of the coherence between discrete quantum states differing in particle number in the sequential transport regime. We find that such a Fock-space coherence can be established when at least one transport channel is available within a quantum-confined structure, and that the evolution of this coherence is decoupled from that of the occupation probabilities of the states, even in the presence of boson-mediated relaxation. Through a systematic analysis, we find quantum interference patterns producing highly resonant regimes where the Fock-space decoherence times are extended significantly, while no resonant regimes are found in the Hilbert-space coherence between states with equal particle numbers. We conclude that the dominant parameters yielding the resonances are the coupling anisotropy to different transport channels as well as the symmetry of the confining barriers.   

Phonon-induced decoherence in donor-based charge qubits

Solid-state based nanostructures have become in recent years promising candidates for the experimental realization of devices in which quantum information can be processed. In this work we study a particular kind of charge qubits in which the information is stored in the lowest orbital states of an electron shared by a pair dopant ions embedded in a silicon crystal. In particular, we investigate the phonon-driven decoherence and its dependence on temperature. The influence of the inter-ion distance on the decoherence process will also be discussed.   

Decoherence in Quantum Magnets: Theory and Experiment on T$_{2}$

The individual properties of molecular magnets are controlled by chemistry rather than nanoengineering, and are highly tunable. This makes them ideal candidates for solid-state qubits. However decoherence in many solid-state systems is anomalously high, and their advantages cannot be exploited until decoherence is understood and suppressed. In molecular magnets decoherence is caused by coupling to the nuclear spin bath, to phonons, and to each other via dipole-dipole and exchange interactions. Here we study decoherence in 2 different crystals of Fe8 nanomolecules, in several field orientations, both theoretically and experimentally. The experimental results for the decoherence time T$_{2}$ agree with the existing theory (Morello et al., Phys Rev Lett 97, 207206 (2006)). To our knowledge this is the first time that experimental decoherence rates agree with theory in magnetic systems.   

Decoherence Suppression of a Solid State Qubit by Uncollapsing

We show that the qubit decoherence due to zero-temperature energy relaxation can be almost completely suppressed by using the quantum uncollapsing procedure. To protect a qubit state, a partial quantum measurement moves it towards the ground state, where it is kept during the storage period, while the second partial measurement restores the initial state. This procedure preferentially selects the cases without energy decay events. Stronger decoherence suppression requires smaller selection probability; a desired point in this trade-off can be chosen by varying the measurement strength. The experimental verification of the uncollapsing procedure has already been performed and using our model we can explain the reported fidelity of this process. The decoherence suppression experiment can be realized in a straightforward way using the superconducting phase qubit, with a minor modification to the experiment that has already been performed.   

Non-Markovian evolution equation of two-time correlation functions of system operators: beyond the quantum regression theorem

Two-time (multiple-time) correlation functions (CF's) are important quantities that can provide more significant information about the system, which the single-time expectation values cannot. In the Markovian open systems, an extremely useful procedure to calculate the two-time (multiple-time) CF's of the system operators is the quantum regression theorem (QRT) that gives a direct relation between the time evolution equation of the single-time expectation values and that of their corresponding two-time (multiple-time) CF's. For the non-Markovian case, it is known that the QRT is not valid in general. Here we present, valid to second order in the system-environment interaction Hamiltonian, a non-Markovian evolution equation of two-time CF's of the system operators at finite environment temperatures for both Hermitian and non-Hermitian system coupling operators and for any initially separable system-environment state (pure or mixed). We then apply the non-Markovian evolution equation to a simple problem of a two-level system coupled to a bosonic environment, as well as to a problem of an exactly solvable pure-dephasing model. The presented evolution equation that generalizes the QRT to the non-Markovian finite-temperature case will have applications in many different branches of physics.   

Decoherence Induced Spontaneous Symmetry Breaking

We study time dependence of exchange symmetry properties of Bell states when two qubits interact with local baths having identical parameters. In case of classical noise, we consider a decoherence Hamiltonian which is invariant under swapping the first and second qubits. We find that as the system evolves in time, two of the three symmetric Bell states preserve their qubit exchange symmetry with unit probability, whereas the symmetry of the remaining state survives with a maximum probability of $ 0.5 $ at the asymptotic limit. Next, we examine the exchange symmetry properties of the same states under local, quantum mechanical noise which is modeled by two identical spin baths. Results turn out to be very similar to the classical case. We identify decoherence as the main mechanism leading to breaking of qubit exchange symmetry. [1] G. Karpat and Z. Gedik, Optics Communications \textbf{282}, 4460 (2009).   

Linear Assignment Maps for Correlated System-Environment States

An assignment map is a mathematical operator that describes initial system-environment states for open quantum systems. We reexamine the notion of assignments, introduced by Pechukas, and show the conditions assignments can account for correlations between the system and the environment, concluding that assignment maps can be made linear at the expense of positivity or consistency is more reasonable. We study the role of other conditions, such as consistency and positivity of the map, and show the effects of relaxing these. Finally, we establish a connection between the violation of positivity of linear assignments and the no-broadcasting theorem.