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See detailMaster equation with quantized atomic motion including dipole-dipole interactions
Damanet, François ULg; Braun, Daniel; Martin, John ULg

Scientific conference (2016, May 26)

We derive a markovian master equation for the internal dynamics of an ensemble of two-level atoms including all effects related to the quantization of their motion [1]. Our equation provides a unifying ... [more ▼]

We derive a markovian master equation for the internal dynamics of an ensemble of two-level atoms including all effects related to the quantization of their motion [1]. Our equation provides a unifying picture of the consequences of recoil and in- distinguishability of atoms beyond the Lamb-Dicke regime on both their dissipative and conservative dynamics, and is relevant for experiments with ultracold trapped atoms. We give general expressions for the decay rates and the dipole-dipole shifts for any motional states, and we find analytical formulas for a number of relevant states (Gaussian states, Fock states and thermal states). In particular, we show that the dipole-dipole interactions and cooperative photon emission can be modulated through the external state of motion. The effects predicted should be experimen- tally observable with Rydberg atoms [2]. [1] F. Damanet, D. Braun, and J. Martin, arXiv:1512.06676v2. [2] K. Afrousheh, P. Bohlouli-Zanjani, D. Vagale, A. Mugford, M. Fedorov, and J. D. D. Martin, Phys. Rev. Lett. 93, 233001 (2004) [less ▲]

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See detailChaotic Bohmian trajectories for stationary states
Cesa, Alexandre ULg; Martin, John ULg; Struyve, Ward

Poster (2016, May 18)

We study the possibility of chaos for the Bohmian dynamics when the wave function is stationary. Examples of stationary wave functions are given for which there is chaos, as demonstrated by numerical ... [more ▼]

We study the possibility of chaos for the Bohmian dynamics when the wave function is stationary. Examples of stationary wave functions are given for which there is chaos, as demonstrated by numerical computations, for one particle moving in 3 spatial dimensions and for two and three entangled particles in 2 dimensions. What is important for the amount of chaos is the overall complexity of the wave function. Some simple measures that partly capture the complexity of the wave function are considered: the participation ratio and different measures of entanglement. We find that these measures often tend to correlate to the amount of chaos. However, the correlation is not perfect, because the measures do not depend on the intrinsic complexity of the states of a given basis. [less ▲]

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See detailSuper- and subradiance from indistinguishable atoms with quantized motion
Damanet, François ULg; Braun, Daniel; Martin, John ULg

Poster (2016, May 18)

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See detailAnticoherence of spin states with point-group symmetries
Baguette, Dorian ULg; Damanet, François ULg; Giraud, Olivier et al

Poster (2016, May 18)

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See detailCollective spontaneous emission with quantized atomic motion
Damanet, François ULg; Braun, Daniel; Martin, John ULg

Scientific conference (2016, May 09)

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See detailMaster equation for collective spontaneous emission with quantized atomic motion
Damanet, François ULg; Braun, Daniel; Martin, John ULg

Scientific conference (2016, March 02)

We derive a markovian master equation for the internal dynamics of an ensemble of two-level atoms including the quantization of their motion. Our equation provides a unifying picture of the effects of ... [more ▼]

We derive a markovian master equation for the internal dynamics of an ensemble of two-level atoms including the quantization of their motion. Our equation provides a unifying picture of the effects of recoil and indistinguishability of atoms beyond the Lamb-Dicke regime on both their dissipative and conservative dynamics. We give general expressions for the decay rates and the dipole-dipole shifts for any motional states, generalizing those in Ref. [1]. We find closed-form formulas for a number of relevant states (gaussian states, Fock states and thermal states). In particular, we show that dipole-dipole interactions and cooperative photon emission [2] can be modulated through the external state of motion. As an application of our general formalism, we study the spatial Pauli blocking of two fermionic atoms beyond the Lamb-Dicke regime [3]. [1] G. S. Agarwal, Springer Tracts In Modern Physics 70, 1 (1974). [2] R. H. Dicke, Phys. Rev. 93, 99 (1954). [3] R. M. Sandner, M. Müller, A. J. Daley & P. Zoller, Phys. Rev. A 84, 043825 (2011). [less ▲]

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See detailAnticoherence of spin states with point-group symmetries
Baguette, Dorian ULg; Damanet, François ULg; Giraud, Olivier et al

Poster (2016, March 02)

We investigate multiqubit permutation-symmetric states with maximal entropy of entanglement. Such states can be viewed as particular spin states, namely anticoherent spin states. Using the Majorana ... [more ▼]

We investigate multiqubit permutation-symmetric states with maximal entropy of entanglement. Such states can be viewed as particular spin states, namely anticoherent spin states. Using the Majorana represen- tation of spin states in terms of points on the unit sphere, we analyze the consequences of a point-group symmetry in their arrangement on the quantum properties of the corresponding state [1]. We focus on the identi cation of anticoherent states (for which all reduced density matrices in the symmetric subspace are maximally mixed) associated with point-group-symmetric sets of points. We provide three di erent characterizations of anticoherence and establish a link between point symmetries, anticoherence, and classes of states equivalent through stochastic local operations with classical communication. We then in- vestigate in detail the case of small numbers of qubits and construct in nite families of anticoherent states with point-group symmetry of their Majorana points, showing that anticoherent states do exist to arbitrary order. [1] D. Baguette et al., Phys. Rev. A 92, 052333 (2015). [less ▲]

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See detailAnticoherence and entanglement of spin states
Martin, John ULg; Baguette, Dorian ULg; Damanet, François ULg et al

Scientific conference (2016, March 02)

We investigate multiqubit permutation-symmetric states with maxi- mally mixed reduced density matrices in the symmetric subspace [1]. Such states can be viewed as particular spin states, namely anticoher ... [more ▼]

We investigate multiqubit permutation-symmetric states with maxi- mally mixed reduced density matrices in the symmetric subspace [1]. Such states can be viewed as particular spin states, namely anticoher- ent spin states [2]. Using the Majorana representation of spin states in terms of points on the unit sphere [3], we analyze the consequences of degeneracies of the Majorana points and of a point-group symmetry in their arrangement on the existence of anticoherent spin states. We provide different characterizations of anticoherence and establish a link between point symmetries, anticoherence, and SLOCC classes [4]. We consider in detail the case of small numbers of qubits and solve the 4-qubit case completely by identifying and characterizing all 4-qubit anticoherent states. [1] D. Baguette, T. Bastin, and J. Martin, Phys. Rev. A 90, 032314 (2014); O. Giraud et al., Phys. Rev. Lett. 114, 080401 (2015); D. Baguette et al., Phys. Rev. A 92, 052333 (2015). [2] J. Zimba, Electron. J. Theor. Phys. 3, 143 (2006). [3] E. Majorana, Nuovo Cimento 9, 43 (1932). [4] SLOCC classes : Classes of states equivalent through stochastic local operations with classical communication. [less ▲]

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See detailMaster equation for collective spontaneous emission with quantized atomic motion
Damanet, François ULg; Braun, Daniel; Martin, John ULg

in Physical Review A (2016), 93

We derive a Markovian master equation for the internal dynamics of an ensemble of two-level atoms including all effects related to the quantization of their motion. Our equation provides a unifying ... [more ▼]

We derive a Markovian master equation for the internal dynamics of an ensemble of two-level atoms including all effects related to the quantization of their motion. Our equation provides a unifying picture of the consequences of recoil and indistinguishability of atoms beyond the Lamb-Dicke regime on both their dissipative and conservative dynamics, and applies equally well to distinguishable and indistinguishable atoms. We give general expressions for the decay rates and the dipole-dipole shifts for any motional states, and we find closed-form formulas for a number of relevant states (Gaussian states, Fock states, and thermal states). In particular, we show that dipole-dipole interactions and cooperative photon emission can be modulated through the external state of motion. [less ▲]

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See detailAnticoherence of spin states with point-group symmetries
Baguette, Dorian ULg; Damanet, François ULg; Giraud, Olivier et al

in Physical Review A (2015), 92

We investigate multiqubit permutation-symmetric states with maximal entropy of entanglement. Such states can be viewed as particular spin states, namely anticoherent spin states. Using the Majorana ... [more ▼]

We investigate multiqubit permutation-symmetric states with maximal entropy of entanglement. Such states can be viewed as particular spin states, namely anticoherent spin states. Using the Majorana representation of spin states in terms of points on the unit sphere, we analyze the consequences of a point-group symmetry in their arrangement on the quantum properties of the corresponding state. We focus on the identification of anticoherent states (for which all reduced density matrices in the symmetric subspace are maximally mixed) associated with point-group-symmetric sets of points. We provide three different characterizations of anticoherence and establish a link between point symmetries, anticoherence, and classes of states equivalent through stochastic local operations with classical communication. We then investigate in detail the case of small numbers of qubits and construct infinite families of anticoherent states with point-group symmetry of their Majorana points, showing that anticoherent states do exist to arbitrary order. [less ▲]

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See detailMultifractality of quantum wave functions in the presence of perturbations
Dubertrand, Rémy ULg; Garcia-Mata, Ignacio; Georgeot, Bertrand et al

in Physical Review. E : Statistical, Nonlinear, and Soft Matter Physics (2015), 92

We present a comprehensive study of the destruction of quantum multifractality in the presence of perturbations. We study diverse representative models displaying multifractality, including a ... [more ▼]

We present a comprehensive study of the destruction of quantum multifractality in the presence of perturbations. We study diverse representative models displaying multifractality, including a pseudointegrable system, the Anderson model, and a random matrix model. We apply several types of natural perturbations which can be relevant for experimental implementations. We construct an analytical theory for certain cases and perform extensive large-scale numerical simulations in other cases. The data are analyzed through refined methods including double scaling analysis. Our results confirm the recent conjecture that multifractality breaks down following two scenarios. In the first one, multifractality is preserved unchanged below a certain characteristic length which decreases with perturbation strength. In the second one, multifractality is affected at all scales and disappears uniformly for a strong-enough perturbation. Our refined analysis shows that subtle variants of these scenarios can be present in certain cases. This study could guide experimental implementations in order to observe quantum multifractality in real systems. [less ▲]

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See detailChaotic Bohmian trajectories for the hydrogen atom
Cesa, Alexandre ULg; Struyve, Ward ULg; Martin, John ULg

Poster (2015, May 13)

In Bohmian mechanics, a single-particle quantum system is described in part by its wave function and in part by the actual position of the particle. The trajectory of the latter can be computed using the ... [more ▼]

In Bohmian mechanics, a single-particle quantum system is described in part by its wave function and in part by the actual position of the particle. The trajectory of the latter can be computed using the guiding equation. This equation states that the velocity of the particle is proportional to the usual probability current associated with its wave function. In this work, we study the quantum trajectory of a single particle in a Coulomb potential whose eigenstates are the well known eigenstates of the hydrogen atom. More precisely, we focus on the relation between chaotic Bohmian trajectories and the motion of wave function nodes. At wave function nodes i.e., where the wave function vanishes, the velocity is not defined which generically induces vorticity. In order to probe chaos, we compute Poincaré map and we numerically evaluate Lyapounov exponents, which characterize the divergence of close trajectories as time increases. For the 2d Coulomb potential, although the superposition of two eigenstates with different energies can lead to an arbitrary high number of moving nodes of the wave function, the Bohmian trajectories display no trace of chaos. This absence of chaotic behaviour originates from the existence of a constant of motion. Therefore, the motion and the number of nodes do not constitute a sufficient condition for the emergence of chaos in Bohmian mechanics. For superpositions of more than two eigenstates, there is no constant of motion, there are moving nodes and we find that the Bohmian trajectories are chaotic. [less ▲]

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See detailAnticoherence of multiqubit symmetric states
Baguette, Dorian ULg; Bastin, Thierry ULg; Martin, John ULg

Conference (2015, May 13)

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See detailTensor Representation of Spin States
Giraud, Olivier; Braun, Daniel; Baguette, Dorian ULg et al

in Physical Review Letters (2015), 114

We propose a generalization of the Bloch sphere representation for arbitrary spin states. It provides a compact and elegant representation of spin density matrices in terms of tensors that share the most ... [more ▼]

We propose a generalization of the Bloch sphere representation for arbitrary spin states. It provides a compact and elegant representation of spin density matrices in terms of tensors that share the most important properties of Bloch vectors. Our representation, based on covariant matrices introduced by Weinberg in the context of quantum field theory, allows for a simple parametrization of coherent spin states, and a straightforward transformation of density matrices under local unitary and partial tracing operations. It enables us to provide a criterion for anticoherence, relevant in a broader context such as quantum polarization of light. [less ▲]

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See detailMultiqubit symmetric states with maximally mixed one-qubit reductions
Baguette, Dorian ULg; Bastin, Thierry ULg; Martin, John ULg

Poster (2014, November 18)

We present a comprehensive study on the remarquable properties shared by maximally entangled symmetric states of arbitrary numbers of qubits in the sense of the maximal mixedness of the one-qubit reduced ... [more ▼]

We present a comprehensive study on the remarquable properties shared by maximally entangled symmetric states of arbitrary numbers of qubits in the sense of the maximal mixedness of the one-qubit reduced density operator. Such states are of great interest in quantum information as they maximize several measures of entanglement, such as Meyer-Wallach entropy [1] and any entanglement monotone based on linear homogenous positive functions of pure state within their SLOCC classes of states [2, 3]. When they exist, they are unique up to local unitaries within their SLOCC classes [3, 4]. They play a specific role in the determination of the local unitary equivalence of multiqubit states [5]. Moreover, they are maximally fragile (in the sense that they are the states which are the most sensitive to noise) and have therefore been proposed as ideal candidates for ultrasensitive sensors [6]. They appear in the litterature under various names : maximally entangled states [6], 1-uniform states [7], normal forms [3, 4] and nongeneric states [5]. We present a general criterion to easily identify whether given symmetric states are maximally entangled or not [9]. We show that these maximally entangled symmetric (MES) states are the only symmetric states for which the expectation value of the associated collective spin S of the system vanishes, which coincides with the definition of anticoherence to order one of spin states. This definition also coincides with the cancellation of the dipole moment of the Husimi function of the state. We then generalize these properties and show that a state is anticoherent to order t, <(S.n)^k> is independent of n for k = 1, . . . , t, where n is a unit vector, iff it has maximally mixed t-qubit reductions or iff all moments up to order 2t of its Husimi function vanish. We also establish the equivalence between anticoherent states to order t and unpolarized light states to order t [8], thereby encompassing various state characterizations under the same banner [9, 10]. We provide a nonexistence criterion allowing us to know immediately whether SLOCC classes of symmetric states can contain MES states or not. We show in particular that the symmetric Dicke state SLOCC classes never contain such MES states, with the only exception of the balanced Dicke state class for even numbers of qubits. We analyze the 4-qubit system exhaustively and identify and characterize all MES states of this system as well as the only 4-qubit state anticoherent to order 2. Finally, we analyze the entanglement content of MES states with respect to the geometric [11] and barycentric [12] measures of entanglement. [1] D. A. Meyer and N. R. Wallach, J. Math. Phys. 43, 4273 (2002). [2] Classes of states equivalent through stochastic local operations with classical communication. [3] F. Verstraete, J. Dehaene, and B. De Moor, Phys. Rev. A 68, 012103 (2003). [4] G. Gour and N. Wallach, N. J. Phys. 13, 073013 (2011). [5] B. Kraus, Phys. Rev. Lett. 104, 020504 (2010). [6] N. Gisin and H. Bechmann-Pasquinucci, Phys. Lett. A 246, 1 (1998). [7] A. J. Scott, Phys. Rev. A 69, 052330 (2004). [8] L. L. Sánchez-Soto, A. B. Klimov, P. de la Hoz, and G. Leuchs J. Phys. B : At. Mol. Opt. Phys. 46, 104011 (2013). [9] D. Baguette, T. Bastin, and J. Martin, Phys. Rev. A 90, 032314 (2014). [10] O. Giraud, D. Braun, D. Baguette, T. Bastin, and J. Martin, arXiv :1409.1106. [11] T.-C. Wei and P. M. Goldbart, Phys. Rev. A 68, 042307 (2003). [12] W. Ganczarek, M. Kus, and K. Zyczkowski, Phys. Rev. A 85, 032314 (2012). [less ▲]

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See detailMultiqubit symmetric states with maximally mixed one-qubit reductions
Baguette, Dorian ULg; Bastin, Thierry ULg; Martin, John ULg

in Physical Review A (2014), 90

We present a comprehensive study of maximally entangled symmetric states of arbitrary numbers of qubits in the sense of the maximal mixedness of the one-qubit reduced density operator. A general criterion ... [more ▼]

We present a comprehensive study of maximally entangled symmetric states of arbitrary numbers of qubits in the sense of the maximal mixedness of the one-qubit reduced density operator. A general criterion is provided to easily identify whether given symmetric states are maximally entangled in that respect or not. We show that these maximally entangled symmetric (MES) states are the only symmetric states for which the expectation value of the associated collective spin of the system vanishes, as well as in corollary the dipole moment of the Husimi function. We establish the link between this kind of maximal entanglement, the anticoherence properties of spin states, and the degree of polarization of light fields. We analyze the relationship between the MES states and the classes of states equivalent through stochastic local operations with classical communication (SLOCC). We provide a nonexistence criterion of MES states within SLOCC classes of qubit states and show in particular that the symmetric Dicke state SLOCC classes never contain such MES states, with the only exception of the balanced Dicke state class for even numbers of qubits. The 4-qubit system is analyzed exhaustively and all MES states of this system are identified and characterized. Finally the entanglement content of MES states is analyzed with respect to the geometric and barycentric measures of entanglement, as well as to the generalized N-tangle. We show that the geometric entanglement of MES states is ensured to be larger than or equal to 1/2, but also that MES states are not in general the symmetric states that maximize the investigated entanglement measures. [less ▲]

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See detailAlteration of decoherence-free states caused by dipole-dipole interactions
Damanet, François ULg; Martin, John ULg

Poster (2014, June 23)

Decoherence, known as the consequence of the coupling of any quantum system to its environment, causes information loss in the system and represents a major problem in the physical realization of quantum ... [more ▼]

Decoherence, known as the consequence of the coupling of any quantum system to its environment, causes information loss in the system and represents a major problem in the physical realization of quantum computers [1]. Decoherence-Free States (DFS) are considered as a possible solution to this problem. A set of trapped cold atoms placed in a DFS state will be immune against decoherence due to spontaneous emission. However, because of dipole-dipole interactions between atoms, induced dephasing effects are likely to destroy the coherence and drive the system out of its DFS [1, 2]. In this work, we study numerically the dynamics of a set of two-level atoms initially in a DFS with respect to dissipative processes by solving the master equation including both dissipative dynamics and dipole dipole interactions. We fo- cus our attention on the infuence of dipolar coupling on the radiated energy rate and coherence of the system as in [3]. In particular, by averaging over many realizations of close randomly distributed atomic positions, we show the formation of a superradiant-like pulse and we study its properties as a function of the dipolar coupling strength. [1] D. A. Lidar & K. B. Whaley, Lectures Notes in Phys., Vol. 622, p83-120, Springer (2003). [2] M. Gross & S. Haroche, Physics reports 93, 301-396 (1982). [3] W. Feng, Y. Li & S-Y. Zhu, Phys. Rev. A 88, 033856 (2013). [less ▲]

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See detailGeneration of artificial magnetic fields using dipole-dipole interactions
Cesa, Alexandre ULg; Martin, John ULg

Poster (2014, June 23)

In 1996, Lloyd [1] showed that the dynamics of complex many-body quantum systems can be efficiently simulated by quantum computers, an idea first put forward by Manin [2] and further developed by Feynman ... [more ▼]

In 1996, Lloyd [1] showed that the dynamics of complex many-body quantum systems can be efficiently simulated by quantum computers, an idea first put forward by Manin [2] and further developed by Feynman [3]. Although the first quantum computers of a few qubits have been realised experimentally [4, 5], the advent of scalable quantum computers might take another few decades. An alternative tool in the context of simulation is a highly controllable quantum system able to mimic the dynamics of other complex quantum systems, known as an analog quantum simulator. Cold neutral atoms and trapped ions have been shown to be versatile quantum simulators [6, 7] thanks to their high flexibility, controllability, and scalability. They permit one to study a wide range of problems arising from atomic physics, relativistic quantum physics, or cosmology [8]. Since neutral atoms do not carry any net charge, the simulation of electric and magnetic condensed matter phenomena, such as the spin Hall effect, seems out of reach. To overcome this apparent difficulty, the idea has been proposed to create artificial electromagnetic potentials for neutral atoms based on atom-light interaction [9– 12]. These artificial potentials act on neutral atoms as real electromagnetic potentials act on charged particles. Many works on artificial gauge potentials induced by atom-light interactions adopt a single-particle approach [12]. The predicted potentials are then supposed to be valid for a system of weakly interacting atoms. So far, the consequences of atom-atom interactions on the generation of artificial gauge fields has little been studied. The aim of this work is to study the artificial gauge fields arising from the interaction of two Rydberg atoms driven by a common laser field [13]. In this situation, we show that the combined atom-atom and atom-field interactions give rise to nonuniform, artificial gauge potentials. We identify the mechanism responsible for the emergence of these gauge potentials. Analytical expressions for the latter indicate that the strongest artificial magnetic fields are reached in the regime intermediate between the dipole blockade regime and the regime in which the atoms are sufficiently far apart such that atom-light interaction dominates over atom-atom interactions. We discuss the differences and similarities of artificial gauge fields originating from resonant dipole-dipole [14] and van der Waals [15] interactions. We also give an estimation of experimentally attainable artificial magnetic fields resulting from this mechanism and we discuss their detection through the deflection of the atomic motion. [1] S. Lloyd, Science 273, 1073 (1996). [2] Yu. I. Manin, Computable and uncomputable, Sovetskoye Radio, Moscow, 1980. [3] R. P. Feynman, Int. J. Theor. Phys. 21, 467 (1982). [4] L. DiCarlo, J. M. Chow, J. M. Gambetta, Lev S. Bishop, B. R. Johnson, D. I. Schuster, J. Majer, A. Blais, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, Nature 460, 240 (2009). [5] N. Xu, J. Zhu, D. Lu, X. Zhou, X. Peng, and J. Du, Phys. Rev. Lett. 108, 130501 (2012). [6] I. Buluta and F. Nori, Science 326, 108 (2009). [7] I. Bloch, J. Dalibard and S. Nascimbéne, Nature Physics 8, 267 (2012). [8] R. Blatt and C. F. Roos, Nature Physics 8, 277 (2012). [9] G. Juzeliunas and P. Öhberg, Phys. Rev. Lett. 93, 033602 (2004). [10] G. Juzeliunas, P. Öhberg, J. Ruseckas, and A. Klein, Phys. Rev. A 71, 053614 (2005). [11] G. Juzeliunas, J. Ruseckas, P. Öhberg, and M. Fleischhauer, Phys. Rev. A 73, 025602 (2006). [12] J. Dalibard, F. Gerbier, G. Juzeliu ̄nas, and P. Öhberg, Rev. Mod. Phys. 83, 1523 (2011). [13] A. Cesa and J. Martin, Phys. Rev. A 88,062703 (2013). [14] A. Gaëtan, Y. Miroshnychenko, T. Wilk, A. Chotia, M. Viteau, D. Comparat, P. Pillet, A. Browaeys, and P. Grangier, Nature Physics 5, 115 (2009). [15] L. Béguin, A. Vernier, R. Chicireanu, T. Lahaye, and A. Browaeys, Phys. Rev. Lett. 110, 263201 (2013). [less ▲]

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See detailSymmetric N-qubit anticoherent states
Baguette, Dorian ULg; Bastin, Thierry ULg; Martin, John ULg

Poster (2014, June 23)

Entanglement is among the key features of quantum mechanics. In the last decade, a lot of efforts has been made to quantify the amount of entanglement of various multipartite states, either pure or mixed ... [more ▼]

Entanglement is among the key features of quantum mechanics. In the last decade, a lot of efforts has been made to quantify the amount of entanglement of various multipartite states, either pure or mixed. In particular, the search for maximally entangled states (states maximizing certain measures of entanglement) has focused a great deal of attention, see e.g. Refs. [1–4]. In this work, we present a comprehensive study of maximally entangled symmetric N-qubit states with respect to the definition of Gisin [1]. According to this definition, a state is maximally entangled if all its one-qubit reduced density matrices are maximally mixed. These states maximize various entanglement measures, such as von Neumann and Meyer-Wallach entropies [5]. They are unique up to local unitaries within the class of states interconvertible under stochastic local operations and classical communication (SLOCC) [3]. Besides, they are conjectured to be maximally entangled with respect to the Negative Partial Transpose measure of entanglement [6]. As appreciated by B. Kraus, they play an important role in the determination of the local unitary equivalence of multiqubit states [7]. Moreover, they are maximally fragile (in the sense that they are the states which are the most sensitive to noise) and therefore have been proposed as ideal candidates for ultrasensitive sensors [1]. We provide general conditions for a symmetric state with an arbitrary number of qubits to be maximally entangled and identify families of SLOCC classes which do not contain any such states. We also compute various measure of entanglement associated with those states in order to characterize them further and find all maximally entangled states up to 4 qubits. We finally prove that maximally entangled states coincide with anticoherent states of order 1. According to the definition of Ref. [8], a symmetric state of N qubits is anticoherent to order t iff 〈(S·n)k〉 is independent of n for k = 1, . . . , t where n is a tridimensional unit vector and S is the collective spin operator associated to the N-qubit system. [1] N. Gisin, H. Bechmann-Pasquinucci, Phys. Lett. A 246 (1998). [2] A. Higuchi, A. Sudbery, Phys. Lett. A, 272, 213 (2000). [3] F. Verstraete, J. Dehaene, B. De Moor, Phys. Rev. A 68, 012103 (2003). [4] J. Martin, O. Giraud, P. A. Braun, D. Braun and T. Bastin, Phys. Rev. A 81, 062347 (2010). [5] D. A. Meyer, N. R. Wallach, J. Math. Phys. 43, 4273 (2002). [6] I. D. K. Brown, S. Stepney, A. Sudbery, and S. L. Braunstein, J. Phys. A 38, 1119 (2005). [7] B. Kraus, Phys. Rev. Lett. 104, 020504 (2010). [8] J. Zimba, EJTP 3, 10 (2006). [less ▲]

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See detailThe two scenarios for quantum multifractality breakdown
Georgeot, Bertrand; Dubertrand, Rémy; Garcia-Mata, Ignacio et al

Scientific conference (2014, June)

Several types of physical systems are characterized by quantum wave func- tions with multifractal properties. In the quantum chaos field, they cor- respond to pseudointegrable systems, with properties ... [more ▼]

Several types of physical systems are characterized by quantum wave func- tions with multifractal properties. In the quantum chaos field, they cor- respond to pseudointegrable systems, with properties intermediate between integrability and chaos. In condensed matter, they include electrons in a disordered potential at the Anderson metal-insulator transition. This multi- fractality leads to particular transport properties and appears in conjunction with specific types of spectral statistics. In parallel, progress in experimental techniques allows to observe finer and finer properties of the wavefunctions of quantum or wave systems, as well as to perform experiments with un- precedented control on the dynamics of the systems studied. In this context, this talk will discuss the robustness of multifractality in presence of footnote- size perturbations. We expose two scenarios for the breakdown of quantum multifractality under the effect of such perturbations. In the first scenario, multifractality survives below a certain scale of the quantum fluctuations. In the other one, the fluctuations of the wave functions are changed at every scale and each multifractal dimension smoothly goes to the ergodic value. We use as generic examples a one-dimensional dynamical system and the three- dimensional Anderson model at the metal-insulator transition, and show that for different types of perturbation the destruction of multifractal properties always follows one of these two ways. Our results thus suggest that quantum multifractality breakdown is universal and obeys one of these two scenarios depending on the perturbation. We also discuss the experimental implica- tions. [less ▲]

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