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arXiv:1309.7715

The entanglement of two qubits coupled ultrastrongly with a quantum oscillator

Tian, Guihua, Shuquan Zhong

Published Sep 30, 2013• 0 citations
arXivHTMLPDF

Abstract

We explore the possibility of the controlled manipulation of the entanglement of two qubits with an external apparatus, the Rabi Hamiltonian. The novel results show that the initially entangled two qubits could have very high probability to stay unchanged by the coherent state of the photon with chosen parameters. If the inter-qubit coupling strength is negative, their entanglement could be kept for a much longer time by a relatively strong external quantum control with the suitable and novel choice of some parameters. Furthermore, their entanglement will not show any sudden death and revival. All these results are different from the previous studies and they are given with reasonable explanations. The maintaining of the entanglement of the two qubits with very high fidelity will be very helpful for the quantum information process.

DOI
10.48550/arxiv.1309.7715

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We explore the possibility of the controlled manipulation of the entanglement of two qubits with an external apparatus, the Rabi Hamiltonian. The novel results show that the initially entangled two qubits could have very high probability to stay unchanged by the coherent state of the photon with chosen parameters. If the inter-qubit coupling strength is negative, their entanglement could be kept for a much longer time by a relatively strong external quantum control with the suitable and novel choice of some parameters. Furthermore, their entanglement will not show any sudden death and revival. All these results are different from the previous studies and they are given with reasonable explanations. The maintaining of the entanglement of the two qubits with very high fidelity will be very helpful for the quantum information process.
The entanglement of two qubits is investigated in the range of their ultra-strongly coupling with a quantum oscillator. The two qubits are initially in four Bell states and they are under the control mechanism of the coherent state of the quantum oscillator. There are four parameters: the average number of the coherent state, the ultra-strong coupling strength, the ratio of two frequencies of qubit and oscillator, and the inter-interaction coupling of the two qubits in the mechanism, and they all are influential parameters on the entanglement of the two qubits. One Bell state |0〉 is easyily kept and is trivial case. The novel results show that there is one state | I 0 〉 among the other three Bell states which the entanglement of the two qubits could be almost completely preserved. The possibility is made into reality by the appropriate choice of the four influential parameters. We give two different schemes to choose the respective parameters to maintain the entanglment of | I 0 〉 almost undiminished. The results will be useful for the quantum information process.
The dynamics of two qubits ultra-strongly coupled with a quantum oscillator is investigated by the adiabatic approximation method. The evolution formula of the initial four Bell states are studied under the control mechanism of the coherent state of the quantum oscillator. The influential parameters for the preservation of the entanglement are the four parameters: the average number of the coherent state, the ultra-strong coupling strength, the ratio of two frequencies of qubit and oscillator, and the inter-interaction coupling of the two qubits. The novel results show that the appropriate choice of these parameters can enable this mechanism to be utilized to preserve the entanglement of the two qubits, which is initially in the state |I_0> of the four Bell states. We give two different schemes to choose the respective parameters to maintain the entangled state |I_0> almost unchanged. The results will be helpful for the quantum information process.
Abstract We investigate the entanglement dynamic behavior of a system with two driven coupled qubits. The effects of the Rabi frequency ratio of nearest qubits, different initial states and different thermal boson number on quantum entanglement are addressed in detail. The results show that, whether the initial state is entangled or not, the two-qubit state will be in a stable entangled state when we select an appropriate parameter for the Rabi frequency ratio. Meanwhile, quantum sudden death and quantum sudden birth can happen in these systems. Increasing the noise strength can also put the system in a stable entanglement state. Hence steady-state entanglement can be obtained by adjusting the parameter of the Rabi frequency ratio and noise strength.
We study the dynamics of two qubits separately sent through two coupled resonators, each initially containing a coherent-state field. We present analytical arguments and numerically approximate solutions for the qubit-field system under different two-qubit initial states, photon-hopping strengths, and detunings. In the far off-resonant regime, the maximal entanglement of two qubits can be generated with the initial qubit state in which one qubit is in the excited state and the other is in the ground state, and the initially maximal two-qubit entanglement can be frozen and fully revived even for large mean photon number. When the qubits are both initially in their excited states or ground states, qubit–qubit entanglement birth and death apparently appear in the regime where the photon-hopping strength is close to qubit-field detuning, and its peaks do not decrease monotonically as the interaction time increases. It is interesting to observe that when there is photon hopping between two fields, the field–field entanglement can be larger than 1 and increases as the initial amplitude of the coherent state grows. Our present setup is fundamental for distributed quantum information processing and applicable to different physical qubit-resonator systems.
The effect of quantum "Bang-Bang" control on entangled states is studied. A system of two initially entangled qubits interacting with a bosonic environment is considered. The interaction induces a loss of the initial entanglement of the two qubits and for specific initial states it causes "entanglement sudden death". A pulsed control of both qubits leads to the preservation of the entanglement. It is also shown that a single pulse performed after the sudden death time induces an entanglement revival in the two qubits system.
We revisit the analytic solution of the two-qubit quantum Rabi model with inhomogeneous coupling and transition frequencies using a displaced oscillator basis. This approach enables us to apply the same truncation rules and techniques adopted in the Rabi model to the two qubits system. The derived analytical spectra match perfectly with the numerical solutions in the parameter regime where the qubits’ transition frequencies are far off-resonance with the field frequency and the interaction strengths reach the ultrastrong coupling regime. We further explore the dynamical behavior of the two qubits as well as the evolution of entanglement. The analytical methods provide unexpectedly accurate results in describing the dynamics of the two qubits in the present experimentally accessible coupling regime. The time evolutions of the probability for the qubits show that the collapse-revival phenomena emerge, survive and finally disappear when one coupling strength increases from weak to strong coupling regimes and the other coupling strength is well into the ultrastrong coupling regime. The inhomogeneous coupling system exhibits new dynamics, which are different from the homogeneous coupling case.