Observation of the algebraic localization-delocalization transition in a 1D disordered potential with a bias force

In a one-dimensional (1D) disordered potential, quantum interferences leading to Anderson lo-calization are ubiquitous, such that all wave-functions are exponentially localized. Moreover, no phase transition toward delocalization is expected in 1D. This behavior is strongly modified in the presence of a bias force. We experimentally study this case, launching a non-interacting 39 K Bose-Einstein condensate in a 1D disordered potential induced by a far-off-resonance laser speckle, while controlling a bias force. In agreement with theoretical predictions, we observe a transition between algebraic localization and delocalization as a function of our control parameter that is the relative strength of the disorder against the bias force. We also demonstrate that the initial velocity of the wave-packet only plays a role through an effective disorder strength due to the correlation of the disorder. Adding a bias force is a quite natural way to probe the transport properties of quantum systems, a subject of broad interest that can be in particular addressed with atomic quantum gases thanks to their high degree of control and versatility [1]. For example, Bloch oscillations has been measured through the addition of a constant force to atoms in periodic potential induced by an optical lattice [2]. A force applied to a harmonic trap is equivalent to a trap displacement. The response to such a displacement permits to reveal the fluid or insulating behavior of atomic systems. In 1D interacting Bose gases, the pinning transition by an optical lattice [3] or the insulating transition in quasi-disordered optical lattice [4, 5] have been studied in this manner. More recently, transport in quantum gases is also studied in junction-type setup more analogous to condensed-matter systems: two reservoirs with different chemical potentials are connected through a constriction. For example, in a gas of fermions, the quantization of conductance through a quantum point contact [6] and the superfluid to normal transition in a disordered thin film have been observed [7]. In our work, we focus on the transport of non-interacting particles in disordered media. Without a bias force, quantum interferences between multiple paths lead to Anderson localization [8] whose signature is an exponential decay in space of single particle wave-function [9]. This phenomenon is ubiquitous in wave/quantum physics and it has been observed in many physical contexts [10] including condensed-matter [11] and ultra-cold atoms [12-14]. One-dimensional truly disordered systems are always localized [15], contrary to the 3D case where a phase transition between localized and extended single particle wave-functions takes place as a function of the disorder strength [16-18]. The localization properties of 1D disordered systems are modified in the presence of a bias force. Theoretical studies predict a transition from algebraic localization to delocalization as a function of a single control non-dimensional parameter α which is the ratio of the force to the disorder strength [19, 20]. Physically, α is the relative energy gain ∆E/E of a particle of energy E when moving over a localization length. Interestingly, in a 1D white noise disorder, this quantity is independent of E as the localization length is proportional to E. If α is small, the force does not considerably change the localization behavior of the particle while for large α its dynamics is severely affected leading to delocalization. This localization-delocalization transition is predicted in the infinite time limit for white noise disorder [20]. In a correlated disorder, as the one produced from a far-off-resonance laser speckle [21], the situation is more complicated. Speckles have no Fourier component beyond a spatial frequency 2k c. As a consequence, back-scattering and localization are not expected in the framework of Born approximation for atoms with wavevectors k > k c [12, 22]. Since localized wave-functions always have a small fraction at long distance corresponding to large energies and momenta in the presence of a bias force, we thus expect correlation-induced delocalization at infinite time. However, signatures of the algebraic localization-delocalization transition are predicted to be observable at transient times [20]. In this paper, we report on the observation of the algebraic localization-delocalization transition with cold-atoms propagating in a one dimensional disordered potential in the presence of a controlled bias force. We experimentally show that the non-dimensional parameter α is the only relevant parameter to describe the transition. We notice that the initial velocity of the quantum wave packet only plays a role through the correlation of the disordered potential, showing that the transition is in-trinsically energy independent. In the localized regime, we demonstrate an algebraic decay of the density and measure the corresponding decay exponent as a function of α. At large disorder strength, a saturation of the exp

Eliminating ground-state dipole moments in quantum optics via canonical transformation

By means of a canonical transformation it is shown how it is possible to recast the equations for molecular nonlinear optics to completely eliminate ground-state static dipole coupling terms. Such dipoles can certainly play a highly important role in nonlinear optical response - but equations derived by standard methods, in which these dipoles emerge only as special cases of transition moments, prove unnecessarily complex. It has been shown that the elimination of ground-state static dipoles in favor of dipole shifts results in a considerable simplification in form of the nonlinear optical susceptibilities. In a fully quantum theoretical treatment the validity of such a procedure has previously been verified using an expedient algorithm, whose defense was afforded only by a highly intricate proof. In this paper it is shown how a canonical transformation method entirely circumvents such an approach; it also affords new insights into the formulation of quantum field interactions.Comment: 18 pages including 1 figur

Diagnostic criteria for constitutional mismatch repair deficiency syndrome: suggestions of the European consortium 'care for CMMRD' (C4CMMRD)

Constitutional mismatch repair deficiency (CMMRD) syndrome is a distinct childhood cancer predisposition syndrome that results from biallelic germline mutations in one of the four MMR genes, MLH1, MSH2, MSH6 or PMS2. The tumour spectrum is very broad, including mainly haematological, brain and intestinal tract tumours. Patients show a variety of non-malignant features that are indicative of CMMRD. However, currently no criteria that should entail diagnostic evaluation of CMMRD exist. We present a three-point scoring system for the suspected diagnosis CMMRD in a paediatric/young adult cancer patient. Tumours highly specific for CMMRD syndrome are assigned three points, malignancies overrepresented in CMMRD two points and all other malignancies one point. According to their specificity for CMMRD and their frequency in the general population, additional features are weighted with 1-2 points. They include multiple hyperpigmented and hypopigmented skin areas, brain malformations, pilomatricomas, a second childhood malignancy, a Lynch syndrome (LS)-associated tumour in a relative and parental consanguinity. According to the scoring system, CMMRD should be suspected in any cancer patient who reaches a minimum of three points by adding the points of the malignancy and the additional features. The diagnostic steps to confirm or refute the suspected diagnosis are outlined. We expect that application of the suggested strategy for CMMRD diagnosis will increase the number of patients being identified at the time when they develop their first tumour. This will allow adjustment of the treatment modalities, offering surveillance strategies for second malignancies and appropriate counselling of the entire family

Tunable three-body interactions in driven two-component Bose-Einstein condensates

International audienceWe propose and demonstrate the appearance of an effective attractive three-body interaction in coherently-driven two-component Bose Einstein condensates. It originates from the spinor degree of freedom that is affected by a two-body mean-field shift of the driven transition frequency. Importantly, its strength can be controlled with the Rabi-coupling strength and it does not come with additional losses. In the experiment, the three-body interactions are adjusted to play a predominant role in the equation of state of a cigar-shaped trapped condensate. This is confirmed though two striking observations: a downshift of the radial breathing mode frequency and the radial collapses for positive values of the dressed-state scattering length

Transform analysis of generalized functions

Transform Analysis of Generalized Functions concentrates on finite parts of integrals, generalized functions and distributions. It gives a unified treatment of the distributional setting with transform analysis, i.e. Fourier, Laplace, Stieltjes, Mellin, Hankel and Bessel Series.Included are accounts of applications of the theory of integral transforms in a distributional setting to the solution of problems arising in mathematical physics. Information on distributional solutions of differential, partial differential equations and integral equations is conveniently collected here.The volume wil

Les conserves alimentaires : fabrication ménagère et industrielle / par L. Lavoine,...

Collection : Encyclopédie des connaissances agricolesContient une table des matièresAvec mode text