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Acta Physica Sinica

Control of maximum evolution speed of quantum states by two-mode entangled light field

Cong Tian, Xiang Lu, Ying-Jie Zhang, Yun‐Jie Xia

Published Jan 1, 2019• 2 citations
Publisher

Abstract

We consider a two-mode entangled coherent light field, in which one mode of the light field is injected into the cavity and interacts with a two-level atom. According to the theory of cavity electrodynamics, the evolution state of atomic system is deduced. Aiming at the dynamic process from the initial state of an atomic system to the target evolution state, the quantum speed limit time is used to characterize the maximum evolution rate of the quantum state of an atomic system. The maximum evolution rate of an atomic system can be controlled by adjusting the coherent parameters of the two-mode entangled coherent light field. But up to now, which kind of quantum speed limit time can be better, universal and strict applicable to the quantum dynamics process of any system is still an unresolved important issue. Based on different methods of measuring the distance between two quantum states and different dynamic evolution channels, many definitions of the quantum speed limit time have been given. The quantum speed limit time proposed by Deffner and Lutz (Deffner S, Lutz E 2013 Phys. Rev. Lett. 111 010402) and the other deduced by Campaioli et al. (Campaioli F, Pollock F A, Binder F C, Modi K 2018 Phys. Rev. Lett. 120 060409; Campaioli F, Pollock F A, Modi K 2018 arXiv:1806.08742) have attracted extensive attention. In this paper, we first compare the advantages of two quantum speed limit times to characterize the maximum evolution rate of quantum states. We find that the quantum speed limit time expression given by Campaioli et al. (Campaioli F, Pollock F A, Modi K 2018 arXiv:1806.08742) in 2018 is a tighter bound when describing the boundary of the shortest time required for the quantum state evolution of a two-level atomic system. Therefore, this paper is mainly based on the quantum speed limit time given by Campaioli et al. to analyze how to achieve the maximum evolution rate of the quantum state of the atomic system by manipulating the parameters of a two-level entangled coherent light field. The results show that the maximum evolution speed of the quantum state of the atomic system can be significantly affected by the coherent parameters of the light field interacting with the atom under certain conditions. Furthermore, when the interacting light field parameters cannot well control the maximum evolution speed of the quantum state, the quantum correlation with the two-mode entangled coherent light field can realize the remote control of the maximum evolution speed of quantum state of atomic system by the light field parameters that are not involved in the atom-light interaction.

DOI
10.7498/aps.68.20190385

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We consider a two-mode entangled coherent light field, in which one mode of the light field is injected into the cavity and interacts with a two-level atom. According to the theory of cavity electrodynamics, the evolution state of atomic system is deduced. Aiming at the dynamic process from the initial state of an atomic system to the target evolution state, the quantum speed limit time is used to characterize the maximum evolution rate of the quantum state of an atomic system. The maximum evolution rate of an atomic system can be controlled by adjusting the coherent parameters of the two-mode entangled coherent light field. But up to now, which kind of quantum speed limit time can be better, universal and strict applicable to the quantum dynamics process of any system is still an unresolved important issue. Based on different methods of measuring the distance between two quantum states and different dynamic evolution channels, many definitions of the quantum speed limit time have been given. The quantum speed limit time proposed by Deffner and Lutz (Deffner S, Lutz E 2013 Phys. Rev. Lett. 111 010402) and the other deduced by Campaioli et al. (Campaioli F, Pollock F A, Binder F C, Modi K 2018 Phys. Rev. Lett. 120 060409; Campaioli F, Pollock F A, Modi K 2018 arXiv:1806.08742) have attracted extensive attention. In this paper, we first compare the advantages of two quantum speed limit times to characterize the maximum evolution rate of quantum states. We find that the quantum speed limit time expression given by Campaioli et al. (Campaioli F, Pollock F A, Modi K 2018 arXiv:1806.08742) in 2018 is a tighter bound when describing the boundary of the shortest time required for the quantum state evolution of a two-level atomic system. Therefore, this paper is mainly based on the quantum speed limit time given by Campaioli et al. to analyze how to achieve the maximum evolution rate of the quantum state of the atomic system by manipulating the parameters of a two-level entangled coherent light field. The results show that the maximum evolution speed of the quantum state of the atomic system can be significantly affected by the coherent parameters of the light field interacting with the atom under certain conditions. Furthermore, when the interacting light field parameters cannot well control the maximum evolution speed of the quantum state, the quantum correlation with the two-mode entangled coherent light field can realize the remote control of the maximum evolution speed of quantum state of atomic system by the light field parameters that are not involved in the atom-light interaction.
A two-level atom drvien by a strong classical field interacts with a single-mode light field, and the interaction between the atom and the light field can turn into an effective anti-Jaynes-Cummings model under the conditions of strong driving and large detuning. In this paper, we mainly study the two-mode entangled coherent light field in this model, in which one mode of the entangled coherent light field interacts with a two-level atom driven by a strong classical field. During the evolution of the total system, we make a selective measurement on the atom. Through tuning the evolution time and the parameter of the coherent field, we can easily control the quantum statistical properties of the other mode of the entangled light fields and generate the expected non-classical light field in a longer interaction time and a wider region of coherent parameter.
The physics system consisting of coherent coupled-atom interaction with coherent single-mode cavity-field is proposed. Using the complete quantum theory, the evolution process of the system is studied. It is found that the quantum atom entangled states and light field entangled states can be transferred into each other under a certain temporal condition. Otherwise, the initial state of the atom or the light field entangled states can be completely preserved by controlling the time of the atoms interaction with the light fields.
The time evolution properties of the quantum fidelity in a system of multi-mode coherent light field resonantly interacting with a two-level atom via any Nj-degenerate N∑-photon transition process are studied by the fully quantum theory and numerical calculations. The analytical expressions of the quantum fidelity of field and atom, and the numerical calculation results for three-mode field interacting with the atom are obtained. Our attention focuses on the discussion of the influences of the initial average photon number, the atomic distribution angle, the phase angle of the atom dipole, the field excitation angle, and the atomic degeneracy on the evolution of the quantum fidelity. The results obtained from the numerical calculation indicate that the above factors lead to the quantum fidelity changing with oscillation behavior. The quantum fidelity of field and atom will drastically decrease as the initial light increases, which is correlated sensitively with the fidelity. The speed change of quantum fidelity is strongly dependent on the atomic degeneracy and the intensity coupling between atoms and fields. The value and frequency of the quantum fidelity change lightly with the atomic distribution angle and the angle of light field excitation as well. The phase angles of the atom dipole almost have no influences on the quantum fidelity of field and atom. According to these properties of the quantum fidelity, we can control the speed and value of quantum fidelity in the system by these constraint conditions.
We investigate the preparation and the control of entangled states in a system with the two-mode coherent fields interacting with a moving two-level atom via the two-photon transition. We discuss entanglement properties between the two-mode coherent fields and a moving two-level atom by using the quantum reduced entropy, and those between the two-mode coherent fields by using the quantum relative entropy. In addition, we examine the influences of the atomic motion and field-mode structure parameter p on the quantum entanglement of the system. Our results show that the period and the duration of the prepared maximal atom-field entangled states and the frequency of maximal two-mode field entangled states can be controlled, and that a sustained entangled state of the two-mode field, which is independent of atomic motion and the evolution time, can be obtained, by choosing appropriately the parameters of atomic motion, field-mode structure, initial state and interaction time of the system.
Under the condition of two-mode squeezed vacuum state field interacting with an atom via the intensity-dependent coupling,the degree of entanglement between the two mode fields is investigated by using quantum relative entropy.It is found that the evolution of degree of two-mode fields entanglement is periodic.When the initial field is strong,the degree of entanglement reach maximum at scaled time gt=kπ(k=0,1,2,…),and the different between the maximum and minimum of the entanglement measures is about 1.3 generally.When the initial field is very weak,the influence of atom initial state on the entanglement evolution is sensitive.And the maximum entanglement appears under the situation of atom in a superposition state of upper level and lower level with equal probability.The entanglement of the two mode fields can be adjusted by controlling the time of the atom passing the cavity and the initial state of the atom.
In the process of a two-mode coherent state field interacting with an atom via intensity-dependent coupling,the evolution of entanglement between the atom and field or between the two-mode field is investigated by using quantum reduced entropy and relative entropy respectively.The results show that we can regulate the above mentioned two kinds of entanglement by choosing the system parameters of the initial state,or controlling the action time between the atom and field.The entanglement of the two-mode field will increase or decrease,but it's impossible to disentangle completely.We can get the EPR state and the separable state between the field and atom periodically in the high field conditions(the average photon number of the field is very large).