Field Entanglement Research Articles

Entanglement and geometric phase of the coherent field interacting with a three two-level atoms in the presence of non-linear terms

We study the interaction of a three two-level atoms (3-2LA) with a one-mode op?tical coherent field in coherent state in the presence of non-linear Kerr medium. The three atoms are initially prepared in upper and entangled states while the field mode is in a coherent state. The constants of motion, 3-2LA and field density matrix are obtained. The analytic results are employed to perform some investigations of the temporal evolution of the von Neumann entropy as measure of the degree of entanglement between the 3-2LA and optical coherent field. The effect of the detuning and the initial atomic states on the evolution of geometric phase and en?tanglement is analyzed. Also, we demonstrate the link between the geometric phase and non-classical properties during the evolution time. Additionally the effect of detuning and initial conditions on the Mandel parameter is studied. The obtained results are emphasize the impact of the detuning and the initial atomic states of the feature of the entanglement, geometric phase and photon statistics of theoptical coherent field.

Entanglement, photon statistics and Wehrl entropy for a time-dependent qubit–field system in the presence of phase decoherence effect

We investigate the effect of qubit motion in terms of speed and acceleration on the variation in dynamic behavior of Wehrl entropy, second order correlation function and qubit–field entanglement. We consider three different coherent states of low-power potential (CSLPP) through the value of its exponent, specifically, the infinite-square, triangular, and harmonic potential wells. The relationship between the photon statistics quantified by the second order correlation function and nonclassical correlation of the qubit–field system is explored as the system evolves. The results show that the proposed scheme is very sensitive to the value of the exponent for both a moving and a stationary qubit. A high correlation between the qubit and CSLPP field is achieved by a proper choice of exponent, qubit speed, and acceleration.

Electro-optic entanglement source for microwave to telecom quantum state transfer

We propose an efficient microwave-photonic modulator as a resource for stationary entangled microwave-optical fields and develop the theory for deterministic entanglement generation and quantum state transfer in multi-resonant electro-optic systems. The device is based on a single crystal whispering gallery mode resonator integrated into a 3D-microwave cavity. The specific design relies on a new combination of thin-film technology and conventional machining that is optimized for the lowest dissipation rates in the microwave, optical, and mechanical domains. We extract important device properties from finite-element simulations and predict continuous variable entanglement generation rates on the order of a Mebit/s for optical pump powers of only a few tens of microwatts. We compare the quantum state transfer fidelities of coherent, squeezed, and non-Gaussian cat states for both teleportation and direct conversion protocols under realistic conditions. Combining the unique capabilities of circuit quantum electrodynamics with the resilience of fiber optic communication could facilitate long-distance solid-state qubit networks, new methods for quantum signal synthesis, quantum key distribution, and quantum enhanced detection, as well as more power-efficient classical sensing and modulation.

Some features of the geometric phase and entanglement of three-level atom under cavity damping effects

In this manuscript, we present a system consisting of a three-level atom interacting with optical field. We investigate qualitatively the entanglement and atomic (field) geometric phase under the effect of cavity damping. The atom–field entanglement is measured by the negativity. We show that these quantifiers depend strongly on the variations of the initial settings of the atom, and this exhibits substantial phenomena that depend on the cavity damping effect. Finally, we explore the link between the entanglement and atomic (field) geometric phase of different physical parameters within the presence and absence of the cavity damping effect.

Pulsed entanglement measured by parametric amplifier assisted homodyne detection.

Balanced homodyne detection relies on a beam splitter to superpose the weak signal input and strong local oscillator. However, recent investigation shows that a high gain phase sensitive amplifier (PSA) can be viewed as homodyne detector, in which the strong pump of PSA serves as the local oscillator [1]. Here, we analyze a new method of measuring the continuous variable entanglement by assisting a balanced homodyne detector with the PSA and implement it experimentally. Before measuring quadrature amplitude with the balanced homodyne detectors, two entangled fields generated from a pulse pumped fiber optical parametric amplifier are simultaneously coupled into the PSA. We find that the normalized noise for both the difference and sum of the quadrature amplitudes of the two entangled fields fall below the shot noise limit by about 4.6 dB, which is the record degree of entanglement measured in optical fiber systems. The experimental results illustrate that the advantages of the new measurement method include but not limit to tolerance to detection loss and characterizing entanglement with only one homodyne detector. The influence of mode-mismatching due to multi-mode property of entanglement on the measured noise reduction can also be greatly mitigated, indicating the new method is advantageous over the traditional measurement in multi-mode case.

Entangling detectors in anti-de Sitter space

We examine in (2+1)-dimensional anti-de Sitter (AdS) space the phenomena of entanglement harvesting — the process in which a pair of detectors (two-level atoms) extract entanglement from a quantum field through local interactions with the field. We begin by reviewing the Unruh-DeWitt detector and its interaction with a real scalar field in the vacuum state, as well as the entanglement harvesting protocol in general. We then examine how the entanglement harvested by a pair of such detectors depends on their spacetime trajectory, separation, spacetime curvature, and boundary conditions satisfied by the field. The harvested entanglement is interpreted as an indicator of field entanglement between the localized regions where the detectors interact with the field, and thus this investigation allows us to probe indirectly the entanglement structure of the AdS vacuum. We find an island of separability for specific values of the detectors’ energy gap and separation at intermediate values of the AdS length for which entanglement harvesting is not possible; an analogous phenomena is observed in AdS4, to which we compare and contrast our results. In the process we examine how the transition probability of a single detector, as a proxy for local fluctuations of the field, depends on spacetime curvature, its location in AdS space, and boundary conditions satisfied by the field.

Entanglement, Complementarity, and Vacuum Fields in Spontaneous Parametric Down-Conversion

Using two crystals for spontaneous parametric down-conversion in a parallel setup, we observe two-photon interference with high visibility. The high visibility is consistent with complementarity and the absence of which-path information. The observations are explained as the effects of entanglement or equivalently in terms of interfering probability amplitudes and also by the calculation of a second-order field correlation function in the Heisenberg picture. The latter approach brings out explicitly the role of the vacuum fields in the down-conversion at the crystals and in the photon coincidence counting. For comparison, we show that the Hong–Ou–Mandel dip can be explained by the same approach in which the role of the vacuum signal and idler fields, as opposed to entanglement involving vacuum states, is emphasized. We discuss the fundamental limitations of a theory in which these vacuum fields are treated as classical, stochastic fields.

Effects of gain saturation on the quantum properties of light in a non-Hermitian gain-loss coupler

Gain saturation is ubiquitous but has not been fully explored in the newly developed field of non-Hermitian optics. On the other hand, the nonclassical properties of light are highly relevant to the gain saturation that influences the quantum noise accompanying light amplification. In this paper, we systematically examine the gain saturation effects in a non-Hermitian system of coupled gain-loss waveguides. We explain the impact of gain saturation on a quantum light field dynamically evolving in the coupled system. In contrast to the ideal situation without gain saturation, one can achieve a quasisteady state under the gain saturation. Moreover, gain saturation reduces the influence of amplification noise and thereby better preserves such quantum features as entanglement. We illustrate the effects of gain saturation by examining the time evolution of the Wigner function, entanglement of the light fields, and the cross-correlation function between the two output modes. Significant differences exist between unsaturated and saturated situations, especially for low photon numbers.

Entanglement protection in Jaynes–Cummings model

In this work, we study the control of dynamics of entanglement and its protection in different Jaynes–Cummings models. To preserve atom–field entanglement in Jaynes–Cummings model and its extension to two-photon Jaynes–Cummings model, we apply a scheme which is based on the parity kick. In fact, the scheme is based on the anti-symmetry properties of the Hamiltonian of system. We also apply the method to protect atom–atom entanglement for a system of two two-level atoms inside a single-mode cavity. The control process of entanglement dynamics is implemented as a sequence of cyclic evolutions and makes it possible to protect the atom–field and atom–atom entanglements for any given initial state with desired long time.

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

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 <i>Phys. Rev. Lett.</i> <b>111</b> 010402) and the other deduced by Campaioli et al. (Campaioli F, Pollock F A, Binder F C, Modi K 2018 <i>Phys. Rev. Lett.</i> <b>120</b> 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.

Deterministic quantum entanglement among multiple quantum nodes

Quantum entanglement is a significant quantum resource, which plays a central role in quantum communication. For realizing quantum information network, it is important to establish deterministic quantum entanglement among multiple spatial-separated quantum memories, and then the stored entanglement is transferred into the quantum channels for distributing and transmitting the quantum information at the user-control time. Firstly, we introduce the scheme of deterministic generation polarization squeezed state at 795 nm. A pair of quadrature amplitude squeezed optical fields are prepared by two degenerate optical parameter amplifiers pumped by a laser at 398 nm, and then the polarization squeezed state of light appears by combining the generated two quadrature amplitude squeezed optical beams on a polarizing beam splitter. Secondly, we present the experimental demonstration of tripartite polarization entanglement described by Stokes operators of optical field. The quadrature tripartite entangled states of light corresponding to the resonance with D1 line of rubidium atoms are transformed into the continuous-variable polarization entanglement via polarization beam splitter with three bright local optical beams. Finally, we propose the generation, storage and transfer of deterministic quantum entanglement among three spatially separated atomic ensembles. By the method of electromagnetically induced transparency light-matter interaction, the optical multiple entangled state is mapped into three distant atomic ensembles to build the entanglement among three atomic spin waves. Then, the quantum noise of entanglement stored in the atomic ensembles is transferred to the three space-seperated quadrature entangled light fields through three quantum channels. The existence of entanglement among the three released beams verifies that the system has the ability to maintain the multipartite entanglement. This protocol realizes the entanglement among three distant quantum nodes, and it can be extended to quantum network with more quantum nodes. All of these lay the foundation for realizing the large-scale quantum network communication in the future.

Theoretical analysis of entanglement enhancement with two cascaded optical cavities

Entanglement source with high entanglement degree is the guarantee for accomplishing the quantum information transmission and process with higher fidelity. Continuous variable Einstein-Podolsky-Rosen (EPR) entangled optical field with quantum correlation of amplitude and phase quadrature is a basic and important quantum resource in the quantum information science area, which can be obtained by a non-degenerate optical parametric amplifier (NOPA) operated below the threshold pump power. Because of the limitation of the imperfect performance of optical components in optical cavity, we should find efficient methods of implementing quantum manipulation to improve the entanglement degree of the entangled state of light. Connecting NOPA1 and NOPA2 in series, the entangled state of light output from the NOPA1 can be manipulated by NOPA2, and the entanglement degree can be enhanced under certain conditions. To improve the entanglement degree to a greater extent, the structure of the NOPA1 is chosen as a half-monolithic standing-wave optical resonator with the triple resonance of the pump and two subharmonic modes. The NOPA1 is able to output the entangled optical fields with an entanglement degree of 8.4 dB, which is the highest entanglement generated by a single device so far. The structure of the NOPA2 can be chosen as a standing-wave optical cavity or a four-mirror ring optical cavity. According to the different structures of the NOPA2, we theoretically design two kinds of optical systems with two cascaded cavities and compare the effects of the two optical systems on the continuous variable EPR entanglement cascaded enhancement in detail. Based on the above contrastive analysis, when the entanglement degree of the input optical fields is 8.4 dB and the transmissivity of the output coupler is lower, the structure of a four-mirror ring optical cavity for NOPA2 cannot enhance the entanglement degree, so the optical system including NOPA2 with standing wave cavity structure and the optical isolator with high transmission efficiency is appropriate. When the transmissivity of the output coupler and transmission efficiency of the optical isolator are higher, the structure of the NOPA2 should be chosen as a standing-wave optical cavity, otherwise the structure of the NOPA2 should be chosen as a four-mirror ring optical cavity. We also theoretically analyze the dependence of the correlation degree of output optical fields on physical parameters. The results show that under the conditions of higher input and output coupling efficiency, higher transmission efficiency and lower intro-cavity loss, the entangled state of light with higher entanglement degree can be obtained experimentally. This provides the reference for obtaining entangled optical fields with higher entanglement degree in the future.

POLITICAL ISLAM AND THE GLOBAL ECONOMY

This article discusses the entanglement of political Islam and the new global economy. It specifically addresses the epistemic fields of political economic concepts of the Islamist organisation of Hizbut Tahrir Indonesia/HTI. This article argues that the organisation offers an entangled epistemic field of religion, politics, and economy. The Islamic concept of khilafah is particularly defined as a new global political and economic systems that challenge the currently dominant capitalist-state of western civilisation. The crucial elements of political economy of the khilafah is the aspect of distribution rather than production, thus the HTI’s criticism lies at the notion of justice and equal access to economic resources and effects. With this framework, the HTI offers a new global political system -based on khilafah- and promises justice in economic distribution.

POLITICAL ISLAM AND THE GLOBAL ECONOMY

This article discusses the entanglement of political Islam and the new global economy. It specifically addresses the epistemic fields of political economic concepts of the Islamist organisation of Hizbut Tahrir Indonesia/HTI. This article argues that the organisation offers an entangled epistemic field of religion, politics, and economy. The Islamic concept of khilafah is particularly defined as a new global political and economic systems that challenge the currently dominant capitalist-state of western civilisation. The crucial elements of political economy of the khilafah is the aspect of distribution rather than production, thus the HTI’s criticism lies at the notion of justice and equal access to economic resources and effects. With this framework, the HTI offers a new global political system -based on khilafah- and promises justice in economic distribution.

Excitation of Atomic Systems by Nonclassical Electromagnetic Fields

Interaction between atomic systems and nonclassical electromagnetic fields is considered using the example of a two-level system. The dynamics of such characteristics as the population of atomic levels, the entanglement of field and atomic subsystems, and the distribution of the number of photons for an active field are investigated.

Rindler-AdS/CFT

In anti-de Sitter space a highly accelerating observer perceives a Rindler horizon. The two Rindler wedges in AdSd+1 are holographically dual to an entangled conformal field theory that lives on two boundaries with geometry ℝ × Hd−1. For AdS3, the holographic duality is especially tractable, allowing quantum-gravitational aspects of Rindler horizons to be probed. We recover the thermodynamics of Rindler-AdS space directly from the boundary conformal field theory. We derive the temperature from the two-point function and obtain the Rindler entropy density precisely, including numerical factors, using the Cardy formula. We also probe the causal structure of the spacetime, and find from the behavior of the one-point function that the CFT “knows” when a source has fallen across the Rindler horizon. This is so even though, from the bulk point of view, there are no local signifiers of the presence of the horizon. Finally, we discuss an alternate foliation of Rindler-AdS which is dual to a CFT living in de Sitter space.

Pure state entanglement harvesting in quantum field theory

Quantum fields in vacuum states carry an infinite amount of quantum entanglement, and its entanglement entropy has the ultraviolet divergence. Harvesting protocols of the vacuum entanglement had been investigated, but its efficiency is very low to date. The main reason of the low efficiency originates from the fact that the extracted entanglement is embedded in a mixed state of two external devices. We propose a general protocol with high efficiency by extracting pure state entanglement from the field. We only use bi-linear interactions between the fields and external devices. Even though the ultraviolet cutoff remains finite, the protocol is capable of extracting a huge amount of entanglement. Hence the infinite amount of entanglement extraction is attained without the ultraviolet divergence of the field entanglement entropy in a continuum limit. There exists a trade-off relation between the extracted entanglement and its energy cost.

Threshold of Non-potential Magnetic Helicity Ratios at the Onset of Solar Eruptions

Abstract The relative magnetic helicity is a quantity that is often used to describe the level of entanglement of non-isolated magnetic fields, such as the magnetic field of solar active regions. The aim of this paper is to investigate how different kinds of photospheric boundary flows accumulate relative magnetic helicity in the corona and if and how well magnetic-helicity-related quantities identify the onset of an eruption. We use a series of three-dimensional, parametric magnetohydrodynamic simulations of the formation and eruption of magnetic flux ropes. All the simulations are performed on the same grid, using the same parameters, but they are characterized by different driving photospheric flows, i.e., shearing, convergence, stretching, and peripheral- and central- dispersion flows. For each of the simulations, the instant of the onset of the eruption is carefully identified by using a series of relaxation runs. We find that magnetic energy and total relative helicity are mostly injected when shearing flows are applied at the boundary, while the magnetic energy and helicity associated with the coronal electric currents increase regardless of the kind of photospheric flows. We also find that, at the onset of the eruptions, the ratio between the non-potential magnetic helicity and the total relative magnetic helicity has the same value for all the simulations, suggesting the existence of a threshold in this quantity. Such a threshold is not observed for other quantities as, for example, those related to the magnetic energy.

Constructing an entangled state in the Heisenberg picture for inflationary cosmology

The effects of the entanglement of the inflaton field which initially entangled with those of another field on observables like power spectrum are known in the context of the Schr\"odinger field theory. To clarify this effect in the Heisenberg picture, there were some attempts to construct the initial entangled state by making use of an entangled transformation (like Bogoliubov transformation) between the Bunch-Davies vacuums and squeezed states. We study the role of the time-dependent entangled transformation in the Schr\"odinger field theory. We derive the relation between two vacuum states which their mode functions are transformed by the entangled transformation in Schr\"odinger picture. We discuss that the time-dependency of the entanglement parameter is inevitable and only in the first order of the entanglement parameter perturbation this time-dependency vanishes. We study the entangled transformation in the Heisenberg picture in term of the entangled parameter which appears in the entangled state in Schr\"odinger picture.

Number-phase uncertainty and quantum dynamics of bosons and fermions interacting with a finite range and large scattering length in a double-well potential

In a previous paper, Das et al (2013 J. Phys. B: At. Mol. Opt. Phys. 46 035501), it was shown that the unitary quantum phase operators play a particularly important role in quantum dynamics of bosons and fermions in a one-dimensional (1D) double-well (DW) when the number of particles is small. In this paper, we define the standard quantum limit (SQL) for phase and number fluctuations, and describe two-mode squeezing for number and phase variables. The usual two-mode number squeezing parameter, also used to describe two-mode entanglement of a quantum field, is defined considering phase as a classical variable. However, when phase is treated as a unitary quantum-mechanical operator, number and phase operators satisfy an uncertainty relation. As a result, the usual definition of number squeezing parameter becomes modified. Two-mode number squeezing occurs when the number fluctuation goes below the SQL at the cost of enhanced phase fluctuation. As an application of number-phase uncertainty, we consider bosons or fermions trapped in a quasi-1D DW potential interacting via a 3D finite-range two-body interaction potential with large scattering length as. Under tight-binding or two-mode approximation, we describe in detail the effects of the range of interaction on the quantum dynamics and number-phase uncertainty in the strongly interacting or unitarity regime . Our results show intriguing coherent dynamics of number-phase uncertainty with number squeezing for bosons and ph squeezing for fermions. Our results may be important for exploring new quantum interferometry, Josephson oscillations, Bose–Hubbard and Fermi–Hubbard physics with ultracold atoms in DW potentials or DW optical lattices. Particularly interesting will be the question of the importance of quantum phase operators in two-atom interferometry and entanglement.