scholarly journals Fast control of interactions in an ultracold two atom system: Managing correlations and irreversibility

2019 ◽  
Vol 6 (2) ◽  
Author(s):  
Thomas Fogarty ◽  
Lewis Ruks ◽  
Jing Li ◽  
Thomas Busch
Keyword(s):  
Particle Interaction ◽  
Interaction Strength ◽  
Von Neumann Entropy ◽  
Particle State ◽  
Particle Interactions ◽  
Interacting Particles ◽  
Von Neumann ◽  
Trapped Bosons ◽  
Fast Control ◽  
Atom System

We design and explore a shortcut to adiabaticity (STA) for changing the interaction strength between two ultracold, harmonically trapped bosons. Starting from initially uncorrelated, non-interacting particles, we assume a time-dependent tuning of the inter-particle interaction through a Feshbach resonance, such that the two particles are strongly interacting at the end of the driving. The efficiency of the STA is then quantified by examining the thermodynamic properties of the system, such as the irreversible work, which is related to the out-of-equilibrium excitations in the system. We also quantify the entanglement of the two-particle state through the von Neumann entropy and show that the entanglement produced in the STA process matches that of the desired target state. Given the fundamental nature of the two-atom problem in ultracold atomic physics, the presented shortcut can be expected to have significant impact on many processes that rely on inter-particle interactions.

scholarly journals Spectral Structure and Many-Body Dynamics of Ultracold Bosons in a Double-Well

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 382
Author(s):  
Frank Schäfer ◽  
Miguel A. Bastarrachea-Magnani ◽  
Axel U. J. Lode ◽  
Laurent de Forges de Parny ◽  
Andreas Buchleitner
Keyword(s):  
Initial Conditions ◽  
Dynamical Behavior ◽  
Particle Interaction ◽  
Interaction Strength ◽  
Von Neumann Entropy ◽  
Spectral Structure ◽  
Many Body ◽  
Point Energy ◽  
Von Neumann ◽  
Body Dynamics

We examine the spectral structure and many-body dynamics of two and three repulsively interacting bosons trapped in a one-dimensional double-well, for variable barrier height, inter-particle interaction strength, and initial conditions. By exact diagonalization of the many-particle Hamiltonian, we specifically explore the dynamical behavior of the particles launched either at the single-particle ground state or saddle-point energy, in a time-independent potential. We complement these results by a characterization of the cross-over from diabatic to quasi-adiabatic evolution under finite-time switching of the potential barrier, via the associated time evolution of a single particle’s von Neumann entropy. This is achieved with the help of the multiconfigurational time-dependent Hartree method for indistinguishable particles (MCTDH-X)—which also allows us to extrapolate our results for increasing particle numbers.

scholarly journals ENTANGLEMENT ENTROPY: HELICITY VERSUS SPIN

2008 ◽  
Vol 06 (01) ◽  
pp. 181-186 ◽  
Author(s):  
SONG HE ◽  
SHUXIN SHAO ◽  
HONGBAO ZHANG
Keyword(s):  
Density Matrix ◽  
Entanglement Entropy ◽  
Specific Form ◽  
Von Neumann Entropy ◽  
Particle State ◽  
Inertial Reference Frame ◽  
Helicity State ◽  
Von Neumann ◽  
Left Handed ◽  
Massive Spin

For a massive spin 1/2 field, we present the reduced spin and helicity density matrix, respectively, for the same pure one particle state. Their relation has also been developed. Furthermore, we calculate and compare the corresponding entanglement entropy for spin and helicity within the same inertial reference frame. Due to the distinct dependence on momentum degree of freedom between spin and helicity states, the resultant helicity entropy is different from that of spin in general. In particular, we find that both helicity entanglement for a spin eigenstate and spin entanglement for a right handed or left handed helicity state do not vanish, and their Von Neumann entropy has no dependence on the specific form of momentum distribution, as long as it is isotropic.

Entanglement for excited states of ultracold bosonic atoms in one-dimensional harmonic traps with contact interaction

2015 ◽  
Vol 29 (30) ◽  
pp. 1550189 ◽  
Author(s):  
Hsuan Tung Peng ◽  
Yew Kam Ho
Keyword(s):  
Quantum Entanglement ◽  
Excited States ◽  
Ground State ◽  
The Other ◽  
Von Neumann Entropy ◽  
Von Neumann ◽  
One Dimensional ◽  
Ultracold Bosonic Atoms ◽  
Bosonic Atoms ◽  
Atom System

We have investigated quantum entanglement for two interacting ultracold bosonic atoms in one-dimensional harmonic traps. The effective potential is modeled by delta interaction. For this two-atom system, we have investigated quantum entanglement properties, such as von Neumann entropy and linear entropy for its ground state and excited states. Using a computational scheme that is different from previously employed, a total of the lowest 16 states are studied. Here we show the dependencies of entanglement properties under various interacting strengths. Comparisons for the ground state entanglement are made with earlier results in the literature. New results for the other 15 excited states are reported here.

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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