Non-Markovian qubit dynamics in a circuit-QED setup

Abstract

We consider a circuit-QED setup that allows the induction and control of non-Markovian dynamics of a qubit. Non-Markovianity is enforced over the qubit by means of its direct coupling to a bosonic mode which is controllably coupled to other qubit-mode system. We show that this configuration can be achieved in a circuit-QED setup consisting of two initially independent superconducting circuits, each formed by one charge qubit and one transmission-line resonator, which are put in interaction by coupling the resonators to a current-biased Josephson junction. We solve this problem exactly and then proceed with a thorough investigation of the emergent non-Markovianity in the dynamics of the qubits. Our study might serve the context for a first experimental assessment of non-Markovianity in a multi-element solid-state device.Comment: 8 pages, 7 figures, slightly changed titl

Time-Dependent Dephasing and Quantum Transport

“…Therefore, investigations of time-dependent dephasing in a transport scenario that includes more general Markovian as well as non-Markovian evolutions have the potential to drive new applications in the context of quantum technologies [ 17 , 18 ]. Furthermore, in recent years, there has been a great interest in the fundamental and practical aspects of non-Markovianity [ 13 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 ]. With the tools resulting from these studies and the experimental advances that have been reported, it is natural to envisage new possibilities to exploit such systems in the context of quantum transport.…”

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“…1). This two-bath model is an appropriate low-energy description of a variety of physical systems and phenomena, such as the excitonic energy transfer process in natural and artificial light-harvesting systems [17], electromagnetic fluctuations of two linear circuits attached to a superconducting qubit [18][19][20], two cavity fields coupled to a SQUID-based charge qubit [21], and the process of thermal transport between two reservoirs coupled with a molecular junction [22]. In the case of zero bias and tunneling, the model exhibits a high level of symmetry, which can be described by a nontrivial central extension of the Abelian symmetry group.…”

Quantum non-Markovianity induced by classical stochastic noise

“…But remember that A and B are not "square" operators, but operators in L(X 1 , X 2 ⊗ Y): they are merely abstract mathematical constructs, and physically the combined action of A and B represents an evolution together with the addition of an ancilla, i.e., an auxilliary system m . Finally, note that what we are actually doing is "stacking" the Kraus operators on top of each other, 47) and that these operators act on an vector |ψ ∈ X 1 as 48) which results in a vector in X 2 ⊗ Y, as would be expected.…”

“…Moving to the Bloch representation, Eq. (3.111) 48) we have that the Bloch vector components, in terms of the matrix coefficients, are n x (t) = ρ 21 (t) + ρ 12 (t), (6.49) n y (t) = −i (ρ 21 (t) − ρ 12 (t)) , (6.50) n z (t) = 2ρ 11 (t) − 1. (6.51) This means that they obey the differential equationṡ…”

“…But rules are rules. (47), complex nanostructures (48) and photosynthetic systems. (49) As can be seen, quantum non-Markovianity is an invaluable resource for quantum technologies, which justifies all the attention it has attracted in recent years.…”