Zheng Duiquan | TUD - Academia.edu (original) (raw)

Papers by Zheng Duiquan

We propose a simple method to generate quantum entanglement between two macroscopic mechanical re... more We propose a simple method to generate quantum entanglement between two macroscopic mechanical resonators in a two-cavity optomechanical system. This entanglement is induced by the radiation pressure of a single photon hopping between the two cavities. Our results are analytical, so that the entangled states are explicitly shown. Up to local operations, these states are two-mode three-component states, and hence the degree of entanglement can be well quantified by the concurrence. By analyzing the system parameters, we find that, to achieve a maximum average entanglement, the system should work in the single-photon strong-coupling regime and the deep-resolved-sideband regime. Quantum entanglement [1,2], as a cornerstone of quantum physics, plays an important role in the foundation of quantum theory and also has potential applications in quantum technology, such as quantum information science [3] and quantum metrology [4]. In particular, how to prepare macroscopic mechanical entanglement is of high interest and significance because such macroscopic entanglement might provide explicit evidence for quantum phenomena [5] and even might possibly help us to clarify the quantum-to-classical transition, as well as the boundary between classical and quantum worlds [6]. Recently, much attention has been paid to the creation of quantum entanglement in macroscopic mechanical systems. Some proposals have been brought forward to generate quantum entanglement in various mechanical resonators [7-22]. In general, we can classify these state-preparation proposals into two categories, according to the coupling channels: either direct coupling or indirect coupling. In the former case, the two mechanical resonators are coupled to each other directly. In the latter case, some kind of an intermediate is needed to induce an effective interaction between the two mechanical resonators. Therefore, the intermediate link should be able to couple with the mechanical resonators. In this sense, cavity optomechanical systems [23-25] can provide a natural platform to induce an interaction between mechanical resonators because there is an intrinsic coupling mechanism between optical and mechanical degrees of freedom. Motivated by this feature, in this paper we propose to study the generation of macroscopic mechanical entanglement in a two-cavity optomechanical system. This system is composed of two coupled optomechanical cavities. In each cavity, the electromagnetic fields couple to the mechanical motion of one moving end mirror. The connection between the two cavity fields is built through a photon-hopping interaction. This photon connection will induce an entanglement between the two mechanical mirrors. We note that some previous studies have considered various entanglements in optomechanical systems [26-32]. In particular, we will focus on the single-photon strong-coupling regime [33-41], in which the radiation pressure of a single photon can produce observable effects. In this regime, people have found that strong photon nonlinearity at the few-photon level (e.g., photon blockade) can be induced by the radiation-pressure coupling [33,38-40]; moreover, resolved phonon sidebands and frequency shifts can be observed in the photon emission and scattering spectra [36]. So, a natural question is whether a single photon can also induce a considerable entanglement between the two mechanical resonators in the single-photon strong-coupling regime. Below, we will address this question by analytically solving the dynamics of the system. Specifically, we consider a two-cavity optomechanical system, which consists of two optomechanical cavities (Fig. 1). Each cavity is formed by a fixed end mirror and a moving one. We focus on a single-mode electromagnetic field in each cavity. This field couples to the mechanical motion of the moving mirror via the radiation-pressure coupling. In addition, the fields in the two cavities couple to each other via a photon-hopping interaction. Without loss of generality, we assume that the two optomechanical cavities are identical. The Hamiltonian of the system is (= 1) H S = j =1,2 [ω c a † j a j + ω M b † j b j − g 0 a † j a j (b † j + b j)] − ξ (a † 1 a 2 + a † 2 a 1), (1) where a j (a † j) and b j (b † j) are, respectively, the annihilation (creation) operators of the single-mode cavity field and the mechanical motion of the moving mirror in the j th (j = 1,2) optomechanical cavity, with respective resonant frequencies ω c and ω M. The parameter g 0 = ω c x zpf /L is the single-photon optomechanical coupling strength, where x zpf = √ 1/(2Mω M) is the zero-point fluctuation of the moving mirror with mass M, and L is the rest length of the cavity. The parameter ξ is the photon-hopping coupling strength between the two cavities. We note that some previous studies have considered multicavity optomechanical systems with only one mechanical resonator [42-48]. To solve the Hamiltonian H S , we first introduce the transformation V 1 = exp[ π 4 (b † 1 b 2 − b † 2 b 1)], and the transformed

We propose a simple method to generate quantum entanglement between two macroscopic mechanical re... more We propose a simple method to generate quantum entanglement between two macroscopic mechanical resonators in a two-cavity optomechanical system. This entanglement is induced by the radiation pressure of a single photon hopping between the two cavities. Our results are analytical, so that the entangled states are explicitly shown. Up to local operations, these states are two-mode three-component states, and hence the degree of entanglement can be well quantified by the concurrence. By analyzing the system parameters, we find that, to achieve a maximum average entanglement, the system should work in the single-photon strong-coupling regime and the deep-resolved-sideband regime. Quantum entanglement [1,2], as a cornerstone of quantum physics, plays an important role in the foundation of quantum theory and also has potential applications in quantum technology, such as quantum information science [3] and quantum metrology [4]. In particular, how to prepare macroscopic mechanical entanglement is of high interest and significance because such macroscopic entanglement might provide explicit evidence for quantum phenomena [5] and even might possibly help us to clarify the quantum-to-classical transition, as well as the boundary between classical and quantum worlds [6]. Recently, much attention has been paid to the creation of quantum entanglement in macroscopic mechanical systems. Some proposals have been brought forward to generate quantum entanglement in various mechanical resonators [7-22]. In general, we can classify these state-preparation proposals into two categories, according to the coupling channels: either direct coupling or indirect coupling. In the former case, the two mechanical resonators are coupled to each other directly. In the latter case, some kind of an intermediate is needed to induce an effective interaction between the two mechanical resonators. Therefore, the intermediate link should be able to couple with the mechanical resonators. In this sense, cavity optomechanical systems [23-25] can provide a natural platform to induce an interaction between mechanical resonators because there is an intrinsic coupling mechanism between optical and mechanical degrees of freedom. Motivated by this feature, in this paper we propose to study the generation of macroscopic mechanical entanglement in a two-cavity optomechanical system. This system is composed of two coupled optomechanical cavities. In each cavity, the electromagnetic fields couple to the mechanical motion of one moving end mirror. The connection between the two cavity fields is built through a photon-hopping interaction. This photon connection will induce an entanglement between the two mechanical mirrors. We note that some previous studies have considered various entanglements in optomechanical systems [26-32]. In particular, we will focus on the single-photon strong-coupling regime [33-41], in which the radiation pressure of a single photon can produce observable effects. In this regime, people have found that strong photon nonlinearity at the few-photon level (e.g., photon blockade) can be induced by the radiation-pressure coupling [33,38-40]; moreover, resolved phonon sidebands and frequency shifts can be observed in the photon emission and scattering spectra [36]. So, a natural question is whether a single photon can also induce a considerable entanglement between the two mechanical resonators in the single-photon strong-coupling regime. Below, we will address this question by analytically solving the dynamics of the system. Specifically, we consider a two-cavity optomechanical system, which consists of two optomechanical cavities (Fig. 1). Each cavity is formed by a fixed end mirror and a moving one. We focus on a single-mode electromagnetic field in each cavity. This field couples to the mechanical motion of the moving mirror via the radiation-pressure coupling. In addition, the fields in the two cavities couple to each other via a photon-hopping interaction. Without loss of generality, we assume that the two optomechanical cavities are identical. The Hamiltonian of the system is (= 1) H S = j =1,2 [ω c a † j a j + ω M b † j b j − g 0 a † j a j (b † j + b j)] − ξ (a † 1 a 2 + a † 2 a 1), (1) where a j (a † j) and b j (b † j) are, respectively, the annihilation (creation) operators of the single-mode cavity field and the mechanical motion of the moving mirror in the j th (j = 1,2) optomechanical cavity, with respective resonant frequencies ω c and ω M. The parameter g 0 = ω c x zpf /L is the single-photon optomechanical coupling strength, where x zpf = √ 1/(2Mω M) is the zero-point fluctuation of the moving mirror with mass M, and L is the rest length of the cavity. The parameter ξ is the photon-hopping coupling strength between the two cavities. We note that some previous studies have considered multicavity optomechanical systems with only one mechanical resonator [42-48]. To solve the Hamiltonian H S , we first introduce the transformation V 1 = exp[ π 4 (b † 1 b 2 − b † 2 b 1)], and the transformed