scholarly journals Entropic analysis of optomechanical entanglement for a nanomechanical resonator coupled to an optical cavity field

2021 ◽  
Vol 4 (3) ◽  
Author(s):  
Jeong Ryeol Choi
Keyword(s):  
Coupling Strength ◽  
Optical Cavity ◽  
Von Neumann Entropy ◽  
Strong Coupling Regime ◽  
Optical Frequency ◽  
Cavity Field ◽  
Quantum Networks ◽  
Nanomechanical Resonator ◽  
Von Neumann ◽  
Quantum Science

We investigate entanglement dynamics for a nanomechanical resonator coupled to an optical cavity field through the analysis of the associated entanglement entropies. The effects of time variation of several parameters, such as the optical frequency and the coupling strength, on the evolution of entanglement entropies are analyzed. We consider three kinds of entanglement entropies as the measures of the entanglement of subsystems, which are the linear entropy, the von Neumann entropy, and the Rényi entropy. The analytic formulae of these entropies are derived in a rigorous way using wave functions of the system. In particular, we focus on time behaviors of entanglement entropies in the case where the optical frequency is modulated by a small oscillating factor. We show that the entanglement entropies emerge and increase as the coupling strength grows from zero. The entanglement entropies fluctuate depending on the adiabatic variation of the parameters and such fluctuations are significant especially in the strong coupling regime. Our research may deepen the understanding of the optomechanical entanglement, which is crucial in realizing hybrid quantum-information protocols in quantum computation, quantum networks, and other domains in quantum science.

scholarly journals Strong optomechanical coupling at room temperature by coherent scattering

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Andrés de los Ríos Sommer ◽  
Nadine Meyer ◽  
Romain Quidant
Keyword(s):  
Strong Coupling ◽  
Coupling Strength ◽  
Room Temperature ◽  
Quantum Control ◽  
Optical Cavity ◽  
Coherent Scattering ◽  
Strong Coupling Regime ◽  
Cavity Decay ◽  
Decoherence Rate ◽  
Optomechanical Coupling

AbstractQuantum control of a system requires the manipulation of quantum states faster than any decoherence rate. For mesoscopic systems, this has so far only been reached by few cryogenic systems. An important milestone towards quantum control is the so-called strong coupling regime, which in cavity optomechanics corresponds to an optomechanical coupling strength larger than cavity decay rate and mechanical damping. Here, we demonstrate the strong coupling regime at room temperature between a levitated silica particle and a high finesse optical cavity. Normal mode splitting is achieved by employing coherent scattering, instead of directly driving the cavity. The coupling strength achieved here approaches three times the cavity linewidth, crossing deep into the strong coupling regime. Entering the strong coupling regime is an essential step towards quantum control with mesoscopic objects at room temperature.

WEHRL ENTROPY OF A MIXED STATE THREE-LEVEL ATOM INTERACTING WITH A CAVITY FIELD

2010 ◽  
Vol 09 (06) ◽  
pp. 623-630
Author(s):  
S. ABDEL-KHALEK ◽  
Y. HASSOUNI ◽  
M. ABDEL-ATY
Keyword(s):  
Mixed State ◽  
Von Neumann Entropy ◽  
Entangled State ◽  
Cavity Field ◽  
Wehrl Entropy ◽  
Von Neumann ◽  
Level Atom ◽  
Total Correlation ◽  
State Case ◽  
Mutual Entropy

In this paper, the Wehrl entropy approach is discussed and compared with the quantum entanglement using a mixed-state three-level atom interacting with a cavity field. In the pure state case, the behavior of the atomic Wehrl entropy shows the same behavior of the entanglement due to the von-Neumann entropy, while the mixed state case gives the total correlation due to quantum mutual entropy. If the system is in an entangled state, the formalism can be used to quantify the entanglement as well as the total correlations.

scholarly journals The Jaynes–Cummings model of a two-level atom in a single-mode para-Bose cavity field

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
H. Fakhri ◽  
M. Sayyah-Fard
Keyword(s):  
Coherent States ◽  
Quantum Noise ◽  
Single Mode ◽  
Von Neumann Entropy ◽  
Cavity Field ◽  
Squeezing Effect ◽  
Atomic Inversion ◽  
Von Neumann ◽  
Level Atom ◽  
Mechanical Nature

AbstractThe coherent states in the parity deformed analog of standard boson Glauber coherent states are generated, which admit a resolution of unity with a positive measure. The quantum-mechanical nature of the light field of these para-Bose states is studied, and it is found that para-Bose order plays an important role in the nonclassical behaviors including photon antibunching, sub-Poissonian statistics, signal-to-quantum noise ratio, quadrature squeezing effect, and multi-peaked number distribution. Furthermore, we consider the Jaynes-Cummings model of a two-level atom in a para-Bose cavity field with the initial states of the excited and Glauber coherent ones when the atom makes one-photon transitions, and obtain exact energy spectrum and eigenstates of the deformed model. Nonclassical properties of the time-evolved para-Bose atom-field states are exhibited through evaluating the fidelity, evolution of atomic inversion, level damping, and von Neumann entropy. It is shown that the evolution time and the para-Bose order control these properties.

scholarly journals Islands in linear dilaton black holes

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Georgios K. Karananas ◽  
Alex Kehagias ◽  
John Taskas
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Entanglement Entropy ◽  
Von Neumann Entropy ◽  
Two Dimensional ◽  
Extremal Case ◽  
Von Neumann ◽  
Dimensional Black Hole ◽  
Linear Dilaton ◽  
Linear Dilaton Black Hole

Abstract We derive a novel four-dimensional black hole with planar horizon that asymptotes to the linear dilaton background. The usual growth of its entanglement entropy before Page’s time is established. After that, emergent islands modify to a large extent the entropy, which becomes finite and is saturated by its Bekenstein-Hawking value in accordance with the finiteness of the von Neumann entropy of eternal black holes. We demonstrate that viewed from the string frame, our solution is the two-dimensional Witten black hole with two additional free bosons. We generalize our findings by considering a general class of linear dilaton black hole solutions at a generic point along the σ-model renormalization group (RG) equations. For those, we observe that the entanglement entropy is “running” i.e. it is changing along the RG flow with respect to the two-dimensional worldsheet length scale. At any fixed moment before Page’s time the aforementioned entropy increases towards the infrared (IR) domain, whereas the presence of islands leads the running entropy to decrease towards the IR at later times. Finally, we present a four-dimensional charged black hole that asymptotes to the linear dilaton background as well. We compute the associated entanglement entropy for the extremal case and we find that an island is needed in order for it to follow the Page curve.

THE UNREASONABLE EFFECTIVENESS OF EXPONENTIALLY SUPPRESSED CORRECTIONS IN PRESERVING INFORMATION

2013 ◽  
Vol 22 (12) ◽  
pp. 1342030 ◽  
Author(s):  
KYRIAKOS PAPADODIMAS ◽  
SUVRAT RAJU
Keyword(s):  
Hilbert Space ◽  
Black Hole ◽  
Quantum Mechanics ◽  
Nonperturbative Effects ◽  
Von Neumann Entropy ◽  
Von Neumann ◽  
Information Theoretic ◽  
Black Hole Evaporation ◽  
Strong Subadditivity ◽  
Unreasonable Effectiveness

We point out that nonperturbative effects in quantum gravity are sufficient to reconcile the process of black hole evaporation with quantum mechanics. In ordinary processes, these corrections are unimportant because they are suppressed by e-S. However, they gain relevance in information-theoretic considerations because their small size is offset by the corresponding largeness of the Hilbert space. In particular, we show how such corrections can cause the von Neumann entropy of the emitted Hawking quanta to decrease after the Page time, without modifying the thermal nature of each emitted quantum. Second, we show that exponentially suppressed commutators between operators inside and outside the black hole are sufficient to resolve paradoxes associated with the strong subadditivity of entropy without any dramatic modifications of the geometry near the horizon.

Generalized information and entanglement entropy, gravitation and holography

2015 ◽  
Vol 30 (16) ◽  
pp. 1530039 ◽  
Author(s):  
O. Obregón
Keyword(s):  
Entanglement Entropy ◽  
Ideal Gas ◽  
Einstein Equations ◽  
Von Neumann Entropy ◽  
Nonextensive Statistical Mechanics ◽  
Von Neumann ◽  
H Theorem ◽  
Gauge Gravity ◽  
Gravity Duality ◽  
Correction Terms

A nonextensive statistical mechanics entropy that depends only on the probability distribution is proposed in the framework of superstatistics. It is based on a Γ(χ2) distribution that depends on β and also on pl. The corresponding modified von Neumann entropy is constructed; it is shown that it can also be obtained from a generalized Replica trick. We further demonstrate a generalized H-theorem. Considering the entropy as a function of the temperature and volume, it is possible to generalize the equation of state of an ideal gas. Moreover, following the entropic force formulation a generalized Newton's law is obtained, and following the proposal that the Einstein equations can be deduced from the Clausius law, we discuss on the structure that a generalized Einstein's theory would have. Lastly, we address the question whether the generalized entanglement entropy can play a role in the gauge/gravity duality. We pay attention to 2d CFT and their gravity duals. The correction terms to the von Neumann entropy result more relevant than the usual UV ones and also than those due to the area dependent AdS3 entropy which result comparable to the UV ones. Then the correction terms due to the new entropy would modify the Ryu–Takayanagi identification between the CFT entanglement entropy and the AdS entropy in a different manner than the UV ones or than the corrections to the AdS3 area dependent entropy.

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