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arXiv:cond-mat/0501581

Time evolution and decoherence of entangled states realized in coupled superconducting flux qubits

Takuya Mouri, Hayato Nakano, Hideaki Takayanagi

Published Jan 25, 2005• 0 citations
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Abstract

We study theoretically how decoherence affects superposition states composed of entangled states in inductively coupled two superconducting flux-qubits. We discover that the quantum fluctuation of an observable in a coupled flux-qubit system plays a crucial role in decoherence when the expectation value of the observable is zero. This examplifies that decoherence can be also induced through a quantum mechanically higher-order effect. We also find that there exists a decoherence free subspace for the environment coupled via a charge degree of freedom of the qubit system.

DOI
10.48550/arxiv.cond-mat/0501581

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We study theoretically how decoherence affects superposition states composed of entangled states in inductively coupled two superconducting flux-qubits. We discover that the quantum fluctuation of an observable in a coupled flux-qubit system plays a crucial role in decoherence when the expectation value of the observable is zero. This examplifies that decoherence can be also induced through a quantum mechanically higher-order effect. We also find that there exists a decoherence free subspace for the environment coupled via a charge degree of freedom of the qubit system.
In two-level approximation, we investigate the influence of mutual inductive coupling in superconducting quantum circuits on the decoherence of flux qubits under sub-Ohmic thermal bath environment by utilizing Bloch-Redfield function. The investigation results show: (1) The memory effect existing in the solid-state environment is beneficial to prolong the decoherence time of the superconducting flux qubit, building sub-Ohmic thermal bath environments can improve the decoherence of the solid-state qubit. (2) When the quantum system and the thermal bath are in weak coupling, generally speaking, the mutual coupling effect between circuit elements will destroy the quantum coherence; but when the quantum system and the thermal bath are in strong coupling, it will help to enhance the decoherence time by controlling the mutual inductive coupling between the loop components.
We have studied decoherence in a system where two Josephson-junction flux qubits share a part of their superconducting loops and are inductively coupled. By tuning the flux-bias condition, we control the sensitivities of the energy levels to flux noises in each qubit. The dephasing rate of the first excited state is enhanced or suppressed depending on the amplitudes and the signs of the sensitivities. We have quantified the 1/f1/f1/f flux noises and their correlations and found that the dominant contribution is by local fluctuations.
In Born-Markov approximation,according to Bloch-Redfield equation,the method to calculate the relaxation time T1 and decoherence time T2 of superconducting qubit is given.Based on this,the decoherence phenomenon of superconducting flux qubit with mutual inductance coupling is investigated.The energy relaxation time T1 and decoherence time T2 of this superconducting qubit is also obtained.The results show that for the flux qubit under investigation,the dephasing time T,the energy relaxation time T1 from high level |j〉 to low level |i〉,and the decoherence time T2 of the quantum system are all proportional to dissipation when other conditions are invariant and the environment thermal bath is equivalent to a pure resistance.
In the Born-Markov approximation and two-level approximation, and using the Bloch-Redfield equation, the decoherence property of superconducting quantum circuit with a flux qubit is investigated.The influence on decoherence of the mutual inductance coupling between the circuit components is complicated.The mutual inductance coupling between different loops will decrease the decoherence time.However, the mutual inductance coupling of the same loop, in a certain interval, will increase the decoherence time.Therefore, we can control the decoherence time by changing the mutual inductance parameters such as the strength and direction of coupling.
We study decoherence effects in qubits coupled to environments that exhibit resonant frequencies in their spectral function. We model the coupling of the qubit to its environment via the Caldeira-Leggett formulation of quantum dissipation/coherence, and study the simplest example of decoherence effects in circuits with resonances such as a dc SQUID phase qubit in the presence of an isolation circuit, which is designed to enhance the coherence time. We emphasize that the spectral density of the environment is strongly dependent on the circuit design, and can be engineered to produce longer decoherence times. We begin with a general discussion of superconducting qubits such as the flux qubit, the Cooper pair box and the phase qubit and show that in these kinds of systems appropriate circuit design can greatly modify the spectral density of the environment and lead to enhancement of decoherence times. In the particular case of the phase qubit, for instance, we show that when the frequency of the qubit is at least two times larger than the resonance frequency of the environmental spectral density, the decoherence time of the qubit is a few orders of magnitude larger than that of the typical ohmic regime, where the frequency of the qubit is much smaller than the resonance frequency of the spectral density. In addition, we demonstrate that the environment does not only affect the decoherence time, but also the frequency of the transition itself, which is shifted from its environment-free value. Second, we show that when the qubit frequency is nearly the same as the resonant frequency of the environmental spectral density, an oscillatory non-Markovian decay emerges, as the qubit and its environment self-generate Rabi oscillations of characteristic time scales shorter than the decoherence time.
The dynamics of two superconducting flux qubits coupled to each other and to a common bath is discussed. We focus on the case in which the qubit-qubit coupling strength dominates over the respective qubit transition frequencies. We derive the master equation including collective effect by modeling the bath as one-dimensional open space in this ultrastrong coupling regime, and find that the coupling greatly modifies both the coherent and the incoherent dynamics of the system, giving rise to qualitatively different properties. By analyzing the steady-state and the dynamics governed by the master equation, we show that ground-state entanglement and maximum coherence between the two qubits can be induced by the environment alone. By employing in addition a single external driving field, both the entangled antisymmetric and symmetric collective states can be populated and preserved with high fidelity. Similarly, entangled states can be prepared using adiabatic passage techniques using two external fields. Our results could find applications in entangling quantum gates and quantum memories free from the decoherence.