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Quantum disentanglement eraser: A cavity QED implementation
Abstract
The Garisto-Hardy disentanglement eraser based on a cavity QED system was presented. The high quality of cavities could be used to realize the new class of quantum erasers referred to as quantum disentanglement erasers. The proposed scheme could also be used for a delayed choice quantum eraser, which allows to acquire single-qubit control over teleportation of an arbitrary binary state. The disentanglement eraser of Garisto and Hardy shows that the entanglement of any two particles that do not interact directly or indirectly, never disappears but encoded in the ancilla of the system.
... As stated above, we initially take two cavity fields in an entangled state (|0 A , 0 B + |1 A , 1 B ) / √ 2 and couple this state with the superposition of the lower atomic transition (|ξ 1 + |ξ 2 ) / √ 2 of a three-level ladder system [9]. This can simply be done by passing the atom through either of the cavities, say cavity B. We assume that the atomic transition |ξ 1 ←→ |ξ 2 is decoupled from the cavity field, whereas the upper level transition |ξ 2 ←→ |ξ 3 only interacts dispersively with it (figure 1). ...
... Thus, as a first step for erasing the tags, we send the auxiliary two-level atoms, initially in their respective ground states |g j with j = 1, 2, through both the cavities where they interact resonantly but independently. The interaction is governed by the interaction picture Hamiltonian [9]: ...
... Now, in order to retrieve and tune these lost fringes in a delayed-choice scenario, we send the auxiliary atoms one by one through the adjustable Ramsey zones R 1 and R 2 , respectively. Such resonant semiclassical atom-field interactions are governed by the Hamiltonian [9]: ...
We present an idea for the doubly tagged delayed-choice tunable quantum eraser in a cavity QED setup, based on fully controlled resonant as well as dispersive atom-field interactions. Two cavity fields, bound initially in the Bell state, are coupled to a three-level atom. Such an atom is initially prepared in the coherent superposition of the lower two levels and is quite capable of exhibiting Ramsey fringes if taken independently. It is shown that the coherence lost due to tagging can not only be retrieved but that the fringe visibility/path distinguishability can also be conditionally tuned in a delayed manner through local manipulation of the entangled cavity fields. The stringent condition here is the retainment of the system's coherence during successive manipulations of the individual cavity fields. Such a quantum eraser, therefore, prominently highlights the links among all the counterintuitive features of quantum theory including the conception of time, measurement, state vector reduction, coherence and information in an unambiguous manner. The schematics can be straightforwardly extended to a multipartite scenario and employed to explore multi-player quantum games with the payoff being strangely decided through delayed choice setups.
... The key element of the protocol is the single-particle interference, whose principle is shown in Figure 14 [95]. The two cavities A and B are prepared in the entangled state as |ϕ 1 = α|0 A |1 B + β|1 A |0 B , where α = |α|e iθa , β = |β|e iθa and |α| 2 + |β| 2 = 1. ...
... The probability P e exhibits one-particle interference fringes. There are two possible paths for the atom to end up in |e , that is it can absorb a photon and transmit to |e in Cavity A or B [95]. The visibility of this interference pattern is 2|αβ|, which coincides with the concurrence of the initial cavity state |ϕ 1 . ...
Concurrence provides us an effective approach to quantify entanglement, which is quite important in quantum information processing applications. In the paper, we mainly review some direct concurrence measurement protocols of the two-qubit optical or atomic system. We first introduce the concept of concurrence for a two-qubit system. Second, we explain the approaches of the concurrence measurement in both a linear and a nonlinear optical system. Third, we introduce some protocols for measuring the concurrence of the atomic entanglement system.
... Before describing our proposed scheme, we briefly review the scheme shown in Fig. 1 that was considered by Zubairy, et al. [31] in their investigation of the quantum disentanglement eraser. In this simple scheme, the concurrence can be directly measured from the visibility for a specific class of entangled state. ...
... The probability P e exhibits one-particle interference fringes, analogous to those of the double-slit pattern, which arise from the fact that there are two possible paths for the atom to end up in |e ; it can absorb a photon and makes a transition to |e in cavity A or in cavity B [31]. The visibility of this interference pattern is 2|αβ|, which coincides with the concurrence of the initial cavity state of Eq. (1). ...
An experimental scheme is proposed that allows direct measurement of the concurrence of a two-qubit cavity system. It is based on the cavity-QED technology using atoms as flying qubits and relies on the identity of the two-particle visibility of the atomic probability with the concurrence of the cavity system. The scheme works for any arbitrary pure initial state of the two-qubit cavity system. Comment: To appear in Physical Review A as a Rapid Comminication
... The decoherence effects take an infinite time evolution under the influence of vacuum while the entanglement vanishes suddenly in a finite time. Some other researchers also investigated the process of disentanglement in the open quantum systems [6]- [9]. The problem of decoherence from spin environments was studied by Cucchietti et al [10], while they considered the spin environments consisting of N independent other than correlated spins . ...
... Also with the vacuum state of environment, the decoherence factors |F ν (t)| = ψ E |U † j U i |ψ E are given by Eq.(14) by the replacements Ω k (n = 0, 1, 2) can be obtained by substituting Λ 0 = λ+g, Λ 1 = λ and Λ 2 = λ−g into Eq. (5) and (6). ...
We study the dynamical process of disentanglement of two qubits and two qutrits coupled to an Ising spin chain in a transverse field, which exhibits a quantum phase transition. We use the concurrence and negativity to quantify entanglement of two qubits and two qutrits, respectively. Explicit connections between the concurrence (negativity) and the decoherence factors are given for two initial states, the pure maximally entangled state and the mixed Werner state. We find that the concurrence and negativity decay exponentially with fourth power of time in the vicinity of critical point of the environmental system. Comment: 8 pages, 6 figures
... In our case, we studied a scheme based on QEDcavities, which was first suggested by Zubairy et al. to examine the Garisto-Hardy disentanglement [22]. Let us assume a two-level atom passes through two consecutive cavities, A and B. However, during its passage, the radiation modes generated by the excited atom are basically coupled to the set of cavity modes. ...
In this paper, we investigate the presence of quantum EPR steering and entanglement, using EPR-Reid and directional
entanglement criteria. In continuous variables, we study the effects of decoherence and thermal noise among the cor-
relations of a joint field-field system. It consists of investigating the interaction between two quantum electrodynamic
cavities during the passage of a two-level atom. Indeed, the main purpose of this paper is to examine the impact of
the decoherence and thermal noise parameters on the behavior of EPR steering and directional entanglement. Hence,
it is shown that the non-classical correlation, including steering and directional entanglement, is sensitive to the vari-
ation of the decoherence and thermal noise parameters. Furthermore, the outcomes provide an evidence about the
asymmetry of steering correlations.
... In order to achieve the desired post-selection, we invert the phase by dispersive interaction of the atom with a high-Q cavity containing fock field, say in general | ⟩, such that this field is only depressively coupled with the transition | 2 ⟩ ⟷ | 3 ⟩ whereas the lower transition | 1 ⟩ ⟷ | 2 ⟩ is no way affected by this field. Such an interaction is governed by dispersive Hamiltonian [40][41][42] ...
Quantum three box paradox is one of the key dynamical mysteries of the quantum evolution explored through Two-State Vector Formalism (TSVF) of the quantum theory in conjunction with the weak measurements. The paradox further deepens the notation of quantum reality while highlighting the strange and counterintutive traits of the quantum unitary evolution in-between two strong measurements. We present an experimentally feasible protocol for implementing the paradox through internal states of a three-level ladder atomic system. The techniques invoked here are all state of the art cavity QED tools and the suggested schematics can be executed practically with good overall results.
... Now, the off-resonant interaction, as mentioned above, is considered under the large detuning limit and the derivation of the effective Hamiltonian for this interaction is given in the Appendix. 19,22 Employing the derived effective Hamiltonian, i.e., ...
A scheme is proposed to study the wave-particle duality of two entangled atoms in a cavity-QED framework. Two atoms may exhibit a mutating trend between particle and wave behaviors. This mutating behavior can be post-selected after the atomic states have been recorded on the state selective detectors. In the present proposal, second Hadamard transformation is always present, whereas the probabilities are the same as that in the case, where the state of the second Hadamard can be controlled by an ancilla. The whole scheme revolves around resonant, off-resonant, and Ramsey interactions of two level atoms with the field. To observe the desired behavior, cavity assisted atom-field multiple swappings are employed for tagging as well as for the better control and good fidelity.
... During its passage through the cavities A and B, the excited atom generates a radiation field of frequency ν (see figure 1). In the interaction picture and rotating-wave approximation, the interaction Hamiltonian takes the following compact form [32,33] as (for more details see appendix A) ...
A realizable model based on the interaction between an excited two-level atom and a radiation field inside two quantum electrodynamics cavities is proposed. It consists of sending the excited atom through two serial cavities that contain the radiation field. Thus, the Lindblad master equations which describe the evolution of the reduced density matrix regarding the radiation field generated from the excited atom inside the cavities are solved in both Markovian and non-Markovian regimes. Therefore, the rate of entanglement inherent in the total field-field system is evaluated using various witnesses by calculating analytically the concurrence and quantum discord, where we illustrate quantitatively the advantage of using an initial EPR and NOON states in the presence of radiation field losses. As an application, a scheme of quantum teleportation using two partial entangled channels is being investigated. Finally, a comparative study between fidelity and the different levels of entanglement of the teleported state in the two regimes is also given.
... Therefore, the dispersive Hamiltonian employed for the purpose just imparts a phase shift to the atom through virtual transitions and does not incorporate any term related to the external center-of-mass motion of the atom. The required Hamiltonian is given as under [64]: ...
Quantum three-box paradox is one of the major mysteries revealed through two-state vector formalism of the quantum theory in conjunction with the weak measurements. We suggest a proposal for the experimental implementation of the paradox using time tested tools of Bragg regime atom optics with a two-level atom diffracted from a cavity field in the momentum space. The proposed schematics can be easily executed within the limits of contemporary laboratory resources using either quantized or classical fields.
... However, let suppose that the radiation fields inside the cavities A and B have the same frequency ν k of k modes (see Fig. (1)). In the interaction picture and by using the rotating-wave approximation, the interaction Hamiltonian takes the following form [36,37] ...
An experimentally realizable model based on the interaction between an excited two-level atom and a radiation field inside two quantum electrodynamics cavities is proposed. It consists of sending an excited two-level atom through two serial cavities which contain the radiation field. Hence, the Lindblad master equation described the reduced density matrix of the joint-joint field system inside the cavities is exactly solved in Markovian and non-Markovian regimes. However, the rate of entanglement inherent in the total field-field system are evaluated using various witnesses of entanglement such as concurrence, logarithmic negativity and quantum discord. Moreover, the non-classicality by means of negativity volume and Wigner function is discussed. Finally, two schemes of quantum teleportation are suggested.
... c The cavity is taken along the yaxis where the atoms have classical momenta, and therefore this interaction does not take into account the corresponding momenta changes, being negligibly minute and feeble. The Hamiltonian describing such an interaction may be expressed as [43]: ...
Hyperentangled states have boosted many quantum informatics tasks tremendously due to their high information content per quantum entity. Until now, however, the engineering and manipulation of such states were limited to photonic systems only. In present article, we propose generating atomic hyperentanglement involving atomic internal states as well as atomic external momenta states. Hypersuperposition, hyperentangled cluster, Bell and Greenberger-Horne-Zeilinger states are engineered deterministically through resonant and off-resonant Bragg diffraction of neutral two-level atoms. Based on the characteristic parameters of the atomic Bragg diffraction, such as comparatively large interaction times and spatially well-separated outputs, such decoherence resistant states are expected to exhibit good overall fidelities and offer the evident benefits of full controllability, along with extremely high detection efficiency, over the counterpart photonic states comprised entirely of flying qubits.
... The unitary evolution of such an off-resonant atom–field system is described by the governing Hamiltonian, written under the dipole and rotating wave approximations along with the assumption of large detuning and is given by[25]; ...
... Yet, it was done for equivalent ensemble states, not for true single system states. The use of single atom high-Q microwave cavities was later proposed to implement the disentanglement eraser [4,7]. ...
By erasing the information about the formation of a bipartite classical
state, it is possible to retrieve two entangled states with opposite parity.
This suggests an analogy between the pairs of properties: entangled-separable
and wave-particle, the latter as it is described in the 'quantum eraser'
scheme. An attainable experiment using photons to demonstrate this effect is
proposed.
... The atom A 1 interacts dispersively with cavity, C 2 , following the Hamiltonian given by H d =~ (ĈĈ y je 1 ihe 1 j Ĉ yĈ jg 1 ihg 1 j). Here = ( 2 d )= is the e¤ective Rabi frequency and d de…nes the atom-…eld coupling for dispersive interaction [28]. This interaction has already been realized experimentally to demonstrate quantum phase gate [29]. ...
Connecting individual quantum systems through quantum channels leads to develop quantum networks crucial to perform multipartite communication or quantum cryptography. We present two techniques to generate entanglement among different parties at larger scale. In the first approach cavity QED technique is used to produce extended entanglement in atomic internal and external degrees of freedom. In this scheme we entangle two tagged atoms in their momentum state with cavity fields. Later, interaction of two auxiliary atoms with the two cavity fields in non-dispersive and dispersive fashion transforms the atoms-fields entanglement to atoms-atoms entanglement. Quantum measurement on auxiliary atoms generates extended entangled state in atomic degrees of freedom. In the second approach we take three cavities in which the two cavities have separate entangled state with third cavity in two modes which are distinguishable. Applying quantum measurement process on third cavity, we develop extended entangled state among the three cavities. We provide experimental parameters to realize the work in laboratory experiment.
... In next step, atom-1 interacts dispersively with the second cavity under the governing Hamiltonian H d =hλ(ĉĉ † |e e|−ĉ †ĉ |g g|). Here λ = μ 2 d / is the effective Rabi frequency with being the atom-field detunning and μ d defines the atom-field coupling for the dispersive interaction [59]. Such an interaction has already been realized to experimentally demonstrate the quantum phase gate [60] and will serve to furnish the remaining part of the Ising interaction in our case. ...
We present an experimentally feasible method, based on currently available cavity QED technology, to generate n-partite linear cluster and graph states in external degree of freedom of atoms. The scheme is based on first tagging n two-level atoms with the respective cavity fields in momentum space. Later on an effective Ising interaction between such tagged atoms, realized through consecutive resonant and dispersive interactions of auxiliary atoms with the remanent cavity fields, can generate the desired atomic momenta states. The procedure is completed when the auxiliary atoms after passing through Ramsey zones are detected in either of their internal states. We also briefly explain the generation of weighted graph states in the atomic external degree of freedom.
... Such a Hamiltonian can, for example, be realized by a single three-level atom in the cascade configuration in the arm C [20,21]. The upper two-levels |a and |b are dispersively coupled to the photon with a detuning ∆ such that η =hg 2 /∆ [22] with g being the atomfield coupling coefficient. ...
We present an analysis of a double Mach-Zehnder interferometer in which an
ensemble of identical pre- and postselected particles leave a weak trace. A
knowledge of the weak value partially destroys the quantum interference. The
results, contrary to some recent claims, are in accordance with the usual
quantum mechanical expectations.
... The decoherence effects take an infinite time evolution under the influence of vacuum noise while the entanglement displays a "sudden death" in a finite time. In their investigations and other studies on disentanglement in open quantum systems [6] [7], only qubit systems are considered. Here, the disentanglement process is characterized by time evolution of the concurrence [8]. ...
We study a dynamic process of disentanglement by considering the
time evolution of bound entanglement for a quantum open system, two
qutrits coupling to a common environment. Here, the initial quantum
correlations of the two qutrits are characterized by the bound
entanglement. Both bosonic and spin environments are considered. We
found that the bound entanglement displays collapses and revivals,
and it can be stable against small temperature and time change. The
thermal fluctuation effects on bound entanglement are also
considered.
... Quantum eraser has been experimentally realized by various people using photons [5,6,7,8,9,10,11], mainly because it is easy to produce entangled photons via spontaneous parametric down conversion (SPDC). There have been some other proposals regarding NMR analogue of quantum eraser [12], neutral kaons [13] and cavity QED [14]. ...
We propose a new setup to demonstrate quantum eraser, using spin-1/2
particles in a modified Stern-Gerlach setup, with a double slit. The
"which-way" information can be erased simply by applying a transverse magnetic
field with an additional magnet, resulting in the emergence of two
complementary staggered interference patterns. Use of the classic Stern-Gerlach
setup, and the unweaving of the washed out interference without any coincident
counting, is what makes this proposal novel.
... Recently, Yu and Eberly [6] have showed that two entangled qubits become completely disentangled in a finite time under the influence of pure vacuum noise. Zubairy et al. [7] have demonstrated how the high quality cavities can be used to realize the new class of quantum erasers referred to as quantum disentanglement erasers. Dodd [5] has studied the competing effects of environmental noise and interparticle coupling on disentanglement by solving the dynamics of two harmonically coupled oscillators. ...
We study the disentanglement of two spin qubits which interact with a general XY spin-chain environment. The dynamical process of the disentanglement is numerically and analytically investigated in the vicinity of quantum phase transition (QPT) of the spin chain in both weak and strong coupling cases. We find that the disentanglement of the two qubits is in general enhanced greatly when the environmental spin chain is exposed to QPT. We give a detailed analysis to facilitate the understanding of the QPT-enhanced decaying behavior of the disentanglement factor. Furthermore, the scaling behavior in the disentanglement dynamics is also revealed and analyzed. Comment: 17 pages, 5 figures
Quantum three box paradox is one of the key dynamical mysteries of the quantum evolution explored through Two-State Vector Formalism (TSVF) of the quantum theory in conjuction with the weak measurements. The paradox further deepens the notation of quantum reality while highlighting the strange and counterintutive traits of the quantum unitary evolution in-between two strong measurements. We present an experimentally feasible protocol for implementing the paradox through internal states of a three-level ladder atomic system. The techniques invoked here are all state of the art cavity QED tools and the suggested schematics can be executed practically with good overall results.
We propose a feasible experiment in the context of cavity QED as follows: The initial state is a maximally entangled two cavity mode (${M}_{A}$, ${M}_{B}$). Next a sequence of atoms are sent, one at a time, and interact with mode ${M}_{B}$. We show that the which-way information is initially stored only in ${M}_{B}$ is now distributed among the parties of the global system. The results realize known complementarity relations derived in the context of arbitrary qubits. We show that this dynamics may lead to a quantum eraser phenomenon provided that measurements of the probe atoms are performed in a basis which maximizes the visibility.
We propose experimentally feasible schemes for deterministic state engineering of a
superposition as well as a variety of entangled states e.g., Bell, GHZ, Cluster and graph states
through exploration of the quantized momenta states of the neutral atoms via distant
manipulations. Such decoherence-resistant, distantly contrived momenta states are realized using
first order, off-resonant Bragg diffraction of the two-level atoms from quantized cavity fields.
The state preparation procedure, along with quantized momenta Bragg interactions, also invokes
usual resonant and dispersive atom-field interactions and culminates deterministically into the
states having overall good fidelities.
We present an analysis of a nested Mach-Zehnder interferometer in which an ensemble of identical pre- and postselected particles leaves a weak trace. A knowledge of the weak value partially destroys the quantum interference. The results, contrary to some recent claims [Vaidman, Phys. Rev. A 87, 052104 (2013)], are in accordance with the usual quantum-mechanical expectations.
We suggest a simple method to generate cluster states of two-level atoms. The protocol utilizes minimum cavity/atomic resources and is based upon standard cavity QED tools alongwith Ramsey technique. Two identical atoms, each initially prepared in coherent superposition, interact simultaneously with an initially vacuum state cavity for a specified time. One atom has resonant interactions while at the same time the other one interacts dispersively. When, after completion of the interaction, cavity is again left into vacuum then atoms are shown to be entangled in bipartite cluster state. The method is also generalized to generate multi-partite linear cluster states as well as the atomic graph states.
Entanglement is one of the key features of the quantum mechanical systems that is fundamentally differen from a classical system, in consequence the dynamical behavior of entangled states is of a great significance. In this paper we investigate the phenomenon of sudden death of entanglement in a bipartite system subjected to squeezed vacuum reservoirs with an arbitrary initial pure entangled state between two fields in the cavities. To estimate the degree of entanglement we use the logarithmic negativity. We show that the sudden death time of the entangled states depends on the initial preparation of the entangled state, the phase shift between them and the parameters of the squeezed vacuum reservoir. We derive the conditions, which assure that The states remain entangled although the interaction with the reservoir. The sudden death time of the entangled states is related to the squeezed parameter of the reservoir and the phase shift between the initial entangled states.
We study the time evolution of decoherence factor of two spin qubits and qutrits coupled to an XY spin chain with Dzyaloshinsky-Moriya (DM) interaction environment. The dynamical process of the decoherence is numerically and analytically investigated. We find that the DM interaction can enhance slightly the decay of the decoherence factor in the weak-coupling region. However, in the strong-coupling region, the decoherence factor is very sensitive to the DM interaction.
We have taken a systematic study of the use of the tools of quantum optics for the implementation of tasks relevant to quantum information and computing. As is widely recognized, the maturation of the field may lead to dramatic improvements in current abilities to process data, communicate securely, and simulate natural processes. Applications range from decoding cryptographic codes and secure key distribution to reducing the complexity of computational problems such as database search and pattern recognition. The key tools we use to accomplish quantum information tasks are coherence in atomic and photonic systems, and the entanglement between correlated subsystems, both of which have been extensively studied in this report.
We suggest a simple method to teleport an unknown superposition of the atomic internal state of a two-level atom onto transverse atomic momenta of another atom during its flight. The scheme relies on the standard cavity QED techniques and is inherently deterministic with sufficiently high fidelity for the teleported state. It is further shown that the procedure can be straightforwardly extended to remotely tune in the probability amplitudes of any atomic momenta multipartite entangled state.
We study entangling and disentangling functions of optical Fourier multiport devices in which input-output relation for the creation and annihilation operators is given by a finite Fourier transform. It is shown that these Fourier multiport devices can act as entanglement converters which can not only create entanglement from an unentangled state at the input but also destroy entanglement in an entangled state at the input. Creation and destruction of two-mode and three-mode entangled coherent states (ECSs) are investigated in detail. The creation and destruction of Bell-type two-mode ECS, GHZ-type and W-type three-mode ECSs are indicated explicitly through using Fourier four-port and six-port devices, respectively.
We propose a scheme for generation of highly non-classical entangled field states of the type 1/root 2(vertical bar n,0 > +/- vertical bar 0, n >) in the cavity QED scenario. The scheme utilizes an atomic analogue of the Mach-Zehnder interferometer having a quantized field in the high-Q cavity containing a superposition of zero and one photon that acts as the first beam splitter. The probability for production of the desired states may approach a value close to unity with high fidelity under prevailing experimental conditions.
We propose two simple and resource-economical schemes for remote preparation of four-partite atomic as well as cavity field cluster states. In the case of atomic state generation, we utilize simultaneous resonant and dispersive interactions of the two two-level atoms at the preparation station. Atoms involved in these interactions are individually pair-wise entangled into two different tri-partite GHZ states. After interaction, the passage of the atoms through a Ramsey zone and their subsequent detection completes the protocol. However, for field state generation we first copy the quantum information in the cavities to the atoms by resonant interactions and then adapt the same method as in the case of atomic state generation. The method can be generalised to remotely generate any arbitrary graph states in a straightforward manner.
We generate highly non-classical entangled two-mode field states of the type by utilizing an atomic analogue of the Mach–Zehnder interferometer, where quantized fields in the high-Q cavities act as beam splitters and mirrors. We discuss that the probability for the production of the desired states may approach a value close to unity under presently available experimental conditions.
A scheme for remote preparation of field (atomic) states is proposed. Protocol execution requires cavity QED based atom-field interactions successively supplemented with Ram-sey interferometry. The state to be remotely prepared at the receiver's end is acquired by deterministically manipulating the sender's component of the pre-shared entangled state. In the case of field entanglement, it is carried out with the help of an atom that passes through the sender's cavity and then traverses a classical external field for spec-ified times prior to detection. However, for atomic entangled states, only interactions with the classical field suffice to complete the task. The scheme guarantees good success probability with high fidelity and requires one bit of classical communication.
We investigate effects of a collective disentanglement eraser performed over
states of two pairs of pre-entangled cavities tagged independently with two
identical three-level atoms. It is shown that the collective disentanglement
operation ensures not only the recovery of initial coherence but also its
extension from the initial two to four qubits, generating four-qubit field
cluster states. We also propose a cavity QED scheme to generate an arbitrary
field graph state by means of a collective operation of disentanglement erasers.
Entanglement plays a crucial role in quantum information protocols, thus the
dynamical behavior of entangled states is of a great importance. In this paper
we suggest a useful scheme that permits a direct measure of entanglement in a
two-qubit cavity system. It is realized in the cavity-QED technology utilizing
atoms as fying qubits. To quantify entanglement we use the concurrence. We
derive the conditions, which assure that the state remains entangled in spite
of the interaction with the reservoir. The phenomenon of sudden death
entanglement (ESD) in a bipartite system subjected to squeezed vacuum reservoir
is examined. We show that the sudden death time of the entangled states depends
on the initial preparation of the entangled state and the parameters of the
squeezed vacuum reservoir.
An experimental scheme is suggested that permits a direct measure of
entanglement in a two-qubit cavity system. It is realized in the cavity-QED
technology utilizing atoms as flying qubits. With this scheme we generate two
different measures of entanglement, namely logarithmic negativity and
concurrence. The phenomenon of sudden death entanglement (ESD) in a bipartite
system subjected to dissipative environment is examined. We show that the
sudden death time of the entangled states depends on the initial preparation of
the entangled state and the temperature of the reservoir.
The quantum eraser effect of Scully and Drühl dramatically underscores the difference between our classical conceptions of time and how quantum processes can unfold in time. Such eyebrow-raising features of time in quantum mechanics have been labeled "the fallacy of delayed choice and quantum eraser" on the one hand and described "as one of the most intriguing effects in quantum mechanics" on the other. In the present paper, we discuss how the availability or erasure of information generated in the past can affect how we interpret data in the present. The quantum eraser concept has been studied and extended in many different experiments and scenarios, for example, the entanglement quantum eraser, the kaon quantum eraser, and the use of quantum eraser entanglement to improve microscopic resolution.
Light detection is usually a destructive process, in that detectors annihilate photons and convert them into electrical signals, making it impossible to see a single photon twice. But this limitation is not fundamental-quantum non-demolition strategies permit repeated measurements of physically observable quantities, yielding identical results. For example, quantum non-demolition measurements of light intensity have been demonstrated, suggesting possibilities for detecting weak forces and gravitational waves. But such experiments, based on nonlinear optics, are sensitive only to macroscopic photon fluxes. The non-destructive measurement of a single photon requires an extremely strong matter-radiation coupling; this can be realized in cavity quantum electrodynamics, where the strength of the interaction between an atom and a photon can overwhelm all dissipative couplings to the environment. Here we report a cavity quantum electrodynamics experiment in which we detect a single photon non-destructively. We use atomic interferometry to measure the phase shift in an atomic wavefunction, caused by a cycle of photon absorption and emission. Our method amounts to a restricted quantum non-demolition measurement which can be applied only to states containing one or zero photons. It may lead to quantum logic gates based on cavity quantum electrodynamics, and multi-atom entanglement.
After they have interacted, quantum particles generally behave as a single nonseparable entangled system. The concept of entanglement plays an essential role in quantum physics. We have performed entanglement experiments with Rydberg atoms and microwave photons in a cavity and tested quantum mechanics in situations of increasing complexity. Entanglement resulted either from a resonant exchange of energy between atoms and the cavity field or from dispersive energy shifts affecting atoms and photons when they were not resonant. With two entangled particles (two atoms or one atom and a photon), we have realized new versions of the Einstein-Podolsky-Rosen situation. The detection of one particle projected the other, at a distance, in a correlated state. This process could be viewed as an elementary measurement, one particle being a âmeterâ measuring the other. We have performed a âquantum nondemolitionâ measurement of a single photon, which we detected repeatedly without destroying it. Entanglement is also essential to understand decoherence, the process accounting for the classical appearance of the macroscopic world. A mesoscopic superposition of states (âSchrödinger catâ) gets rapidly entangled with its environment, losing its quantum coherence. We have prepared a Schrödinger cat made of a few photons and studied the dynamics of its decoherence, in an experiment which constitutes a glimpse at the quantum/classical boundary. We have also investigated entanglement as a resource for the processing of quantum information. By using quantum two-state systems (qubits) instead of classical bits of information, one can perform logical operations exploiting quantum interferences and taking advantage of the properties of entanglement. Manipulating as qubits atoms and photons in a cavity, we have operated a quantum gate and applied it to the generation of a complex three-particle entangled state. We finally discuss the perspectives opened by these experiments for further fundamental studies.
We have observed an effect known as a quantum eraser, using a setup similar to one previously employed to demonstrate a violation of Bell's inequalities. In this effect, an interfering system is first rendered incoherent by making the alternate Feynman paths which contribute to the overall process distinguishable; with our apparatus this is achieved by placing a half wave plate in one arm of a Hong-Ou-Mandel interferometer so as to rotate the polarization of the light in that arm by 90°. This adds information to the system, in that polarization is a new parameter which serves to label the path of a given photon, even after a recombining beam splitter. The quantum ``eraser'' removes this information from the state vector, after the output port of the interferometer, but in time to cause interference effects to reappear upon coincidence detection. For this purpose, we use two polarizers in front of our detectors. We present experimental results showing how the degree of erasure (which determines the visibility of the interference) depends on the relative orientation of the polarizers, along with theoretical curves. In addition, we show how this procedure may do more than merely erase, in that the act of ``pasting together'' two previously distinguishable paths can introduce a new relative phase between them.
An unknown quantum state ‖φ〉 can be disassembled into, then later reconstructed from, purely classical information and purely nonclassical Einstein-Podolsky-Rosen (EPR) correlations. To do so the sender, ‘‘Alice,’’ and the receiver, ‘‘Bob,’’ must prearrange the sharing of an EPR-correlated pair of particles. Alice makes a joint measurement on her EPR particle and the unknown quantum system, and sends Bob the classical result of this measurement. Knowing this, Bob can convert the state of his EPR particle into an exact replica of the unknown state ‖φ〉 which Alice destroyed.
We report a delayed "choice" quantum eraser experiment of the type proposed by Scully and Druhl (where the "choice" is made randomly by a photon at a beam splitter). The experimental results demonstrate the possibility of delayed determination of particlelike or wavelike behavior via quantum entanglement. The which-path or both-path information of a quantum can be marked or erased by its entangled twin even after the registration of the quantum.
We report the implementation of a three-spin quantum disentanglement eraser on a liquid-state NMR quantum information processor. A key feature of this experiment was its use of pulsed magnetic field gradients to mimic projective measurements. This ability is an important step towards the development of an experimentally controllable system which can simulate any quantum dynamics, both coherent and decoherent.
We propose and analyze an experiment designed to probe the extent to which information accessible to an observer and the "eraser" of this information affects measured results. The proposed experiment could also be operated in a "delayed-choice" mode.
Recently, Mohrhoff [Am. J. Phys. 64, 1468-1475 (1996)] has analyzed a thought experiment of ours [Nature (London) 351, 111-116 (1991)] where a double-slit interferometer for atoms is supplemented by a pair of which-way detectors. Owing to the quantum nature of these detectors, the experimenter can choose between acquiring which-way knowledge and observing an interference pattern. The latter option makes use of a procedure called ``quantum erasure.'' Mohrhoff (along with other bright colleagues who have made similar statements) claims erroneously that the experimenter has to make this choice before the atom hits the screen. We readdress this issue here and demonstrate that our original assertion was correct: The experimenter can choose between which-way knowledge and quantum erasure at any time, even after the atom has left its mark on the screen.
The principle of complementarity refers to the ability of
quantum-mechanical entities to behave as particles or waves under
different experimental conditions. For example, in the famous
double-slit experiment, a single electron can apparently pass through
both apertures simultaneously, forming an interference pattern. But if a
`which-way' detector is employed to determine the particle's path, the
interference pattern is destroyed. This is usually explained in terms of
Heisenberg's uncertainty principle, in which the acquisition of spatial
information increases the uncertainty in the particle's momentum, thus
destroying the interference. Here we report a which-way experiment in an
atom interferometer in which the `back action' of path detection on the
atom's momentum is too small to explain the disappearance of the
interference pattern. We attribute it instead to correlations between
the which-way detector and the atomic motion, rather than to the
uncertainty principle.
We have realized a quantum phase gate operating on quantum bits carried by a single Rydberg atom and a zero- or one-photon field in a high- Q cavity. The gate operation is based on the dephasing of the atom-field state produced by a full cycle of quantum Rabi oscillation. The dephasing angle, conditioned to the initial atom-field state, can be adjusted over a wide range by tuning the atom-cavity frequency difference. We demonstrate that the gate preserves qubit coherence and generates entanglement. This gate is an essential tool for the nondestructive measurement of single photons and for the manipulation of many-qubit entanglement in cavity QED.
In a recent contribution to this journal [Am. J. Phys. 64, 1468-1475 (1996)] I wrongly asserted that retrocausation in the Englert, Scully, and Walther (ESW) experiment (a double-slit interference experiment with atoms) can occur only until the atom arrives at the screen. In their response, Englert, Scully, and Walther [preceding paper] point out my fallacy but give an incomplete analysis of its origin. In this paper I trace this fallacy to a deep-seated preconception about time and reality. I show that among the two possible realistic interpretations of standard quantum mechanics, the reality-of-states view and the reality-of-phenomena view, only the latter is viable. It follows that retrocausation is a necessary feature of any realistic account of the ESW experiment based on standard quantum mechanics. Finally I eludicate the sense in which the spatial properties of quantum systems are objective, and show that they are extrinsic rather than intrinsic.
A two-slit experiment with atoms, proposed by Englert, Scully, and Walther, appears to permit experimenters to choose, after each atom has made its mark on the screen, whether the atom has passed through a particular slit or has, in some sense, passed through both of them. Through a misleading wording these authors even appear to endorse this interpretation. In actual fact, this choice exists only until the atom hits the screen. The said experiment thus is a ``delayed-choice'' experiment only in the semantically contingent sense of Wheeler.
In the present paper we expand upon ideas published some time ago in connection with which path detectors based on the micromaser. Frequently questions arise concerning the time ordering of detection and eraser events. We here show, by a detailed and careful analysis of a quantum eraser experimental setup, that the experimenter can choose to ascertain particle-like which path information or wavelike interference information even after the atom has hit the screen.
We report the implementation of two- and three-spin quantum erasers using nuclear magnetic resonance (NMR). Quantum erasers provide a means of manipulating quantum entanglement, an important resource for quantum information processing. Here, we first use a two-spin system to illustrate the essential features of quantum erasers. The extension to a three-spin “disentanglement eraser” shows that entanglement in a subensemble can be recovered if a proper measurement of the ancillary system is carried out. Finally, we use the same pair of orthogonal decoherent operations used in quantum erasers to probe the two classes of entanglement in tripartite quantum systems: the Greenberger-Horne-Zeilinger state and the W state. A detailed presentation is given of the experimental decoherent control methods that emulate the loss of phase information in strong measurements, and the use of NMR decoupling techniques to implement partial trace operations.
Simultaneous observations of wave and particle behavior is prohibited,
usually by the position-momentum uncertainty relation. It is reported
here, however, that a way has been found, based on matter-wave
interferometry and recent advances in quantum optics, to obtain
which-path or particlelike information without scattering or otherwise
introducing large uncontrolled phase factors into the interfering beams.
It is the information contained in a functioning measuring apparatus,
rather than controllable alterations of the spatial wave function, that
changes the outcome of the experiment to enforce complementarity.
We propose a simple method to test Bohr complementarity in the context of cavity QED. When an atom is sent through two resonant classical fields, the probability of finding the atom in definite states exhibit interference fringes. Replacing the first classical field with a quantized cavity field, the interference is destroyed since the which-path information for the atom reaching a definite state is recorded in the cavity. The associated quantum eraser can also be realized.
An interferometer in which an atom traverses two identical micromaser cavities in succession is proposed. Depending on the preparation of the cavity fields, the probability for finding the atom in a definite final state displays Ramsey fringes or not. If the initial cavity fields are such that the state of the atom between the cavities can be determined, then the Ramsey fringes disappear, as is required by the principle of complementarity.
Implementing the ideas of Bennett et al. [Phys. Rev. Lett. 70, 1895 (1993)], we present an experimentally feasible scheme for the teleportation of an unknown atomic state between two high-Q cavities containing a nonlocal quantum superposition of microwave field states. This experiment provides alternative tests of quantum nonlocality involving high-order atomic correlations.
The exchange of photons between single Rydberg atoms and a single mode of a superconducting cavity with a quality factor Q = 8 x 10 to the 8th at 2 K was observed. Signals could still be detected with an average number of only 0.06 atom simultaneously in the cavity. With one Rydberg atom the linewidth of the maser transition at about 21 GHz was power broadened, and at high densities asymmetry of the transition was observed which is ascribed to an ac Stark effect.
Second-order interference is observed in the superposition of signal photons from two coherently pumped parametric down-converters, when the paths of the idler photons are aligned. The interference exhibits certain nonclassical features; it disappears when the idlers are misaligned or separated by a beam stop. The interpretation of this effect is discussed in terms of the intrinsic indistinguishability of the photon paths.
To illustrate the quantum mechanical principle of complementarity, Bohr described an interferometer with a microscopic slit that records the particle's path. Recoil of the quantum slit causes it to become entangled with the particle, resulting in a kind of Einstein-Podolsky-Rosen pair. As the motion of the slit can be observed, the ambiguity of the particle's trajectory is lifted, suppressing interference effects. In contrast, the state of a sufficiently massive slit does not depend on the particle's path; hence, interference fringes are visible. Although many experiments illustrating various aspects of complementarity have been proposed and realized, none has addressed the quantum-classical limit in the design of the interferometer. Here we report an experimental investigation of complementarity using an interferometer in which the properties of one of the beam-splitting elements can be tuned continuously from being effectively microscopic to macroscopic. Following a recent proposal, we use an atomic double-pulse Ramsey interferometer, in which microwave pulses act as beam-splitters for the quantum states of the atoms. One of the pulses is a coherent field stored in a cavity, comprising a small, adjustable mean photon number. The visibility of the interference fringes in the final atomic state probability increases with this photon number, illustrating the quantum to classical transition.
We define a new measurement of entanglement, the entanglement of projection, and find that it is natural to write the entanglements of formation and assistance in terms of it. Our measure allows us to describe a new class of quantum erasers which restore entanglement rather than just interference. Such erasers can be implemented with simple quantum computer components. We propose realistic optical versions of these erasers. Comment: 12pp, 2 figs, LATEX (Revtex)