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Experimental recordings of the near (left) and far (right) fields under different detunings measured in percentage of the free spectral range. Also the voltage applied on the piezomirror PM2 is indicated.
Source publication
Spontaneous transverse pattern formation is experimentally studied in a
BaTiO3 photorefractive oscillator under degenerate four-wave
mixing conditions. A near self-imaging resonator of high Fresnel number
and quasi-one-dimensional in the transverse plane is used. A fine
control technique of the cavity detuning, Ω , is described. It
allows a precise...
Contexts in source publication
Context 1
... voltage was changed in 1 V steps in order to study the behavior of the spatial patterns with detuning. Recording time was about 1 min to avoid the possible detuning shift due to the drift of the active resonator. An example of the so- obtained patterns is shown in Fig. 3 corresponding to de- creasing voltage values (decreasing cavity frequencies) from (a) to (k). A homogeneous state (a), a domain wall (b), and periodic stripes (g)-(j) are shown, which are connected by a series of nonperiodic striped patterns (c)-(f). All these pat- terns are steady, except the transient competition between rolls of ...
Context 2
... understanding the behavior of the system. Figure 6 corresponds to one of the series shown in Fig. 4, but now the horizontal axis is detuning measured in units of % FSR (let us call it ). For negative detuning (ranging from −90% FSR to 0 % FSR) stripes are observed, being pe- riodic rolls in region A and nonperiodic patterns in region B [like in Figs. 3(c)-3(f)]. At zero and positive we observe Only the main elements are depicted. PM4' and M1' are the image planes of PM4 and M1 (see Fig. 1) through the corresponding telescopes and beam splitters. The distances l 1 and l 2 are oriented, being positive (negative) if they point to the right (left). The length of the crystal is denoted by d. The ...
Context 3
... as a function of the transverse wave number, and the bottom row displays the associated density plots of the predicted far-field pattern according to Eq. 14. Note that the predicted far fields compare well with our experimen- tal observations see Fig. 3. Especially note, around zero detuning, how a set of tilted waves also the on-axis one (14); d 1 and d 2 denote the borders of the slits located at the Fourier plane. In all figures the horizontal axis corresponds to k and its size is indicated. Each column corresponds to a given cavity detuning marked on the top. For details, see Sec. ...
Context 4
... set of tilted waves also the on-axis one (14); d 1 and d 2 denote the borders of the slits located at the Fourier plane. In all figures the horizontal axis corresponds to k and its size is indicated. Each column corresponds to a given cavity detuning marked on the top. For details, see Sec. V. can be oscillating. Therefore we expect, and observe Fig. 3, dissipative structures, but they are not periodic as the wave-number selection mechanism given by the cavity does not work in a clean way here. Clearly the above is a linear reasoning but we have checked experimentally that these nonperiodic patterns are not a transient stage: some spots can change their intensity as well as their ...
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Citations
... This novel setup is inspired by earlier theoretical proposals [32][33][34][80][81][82]. Such transverse self-organization has been observed in nearly degenerate Fabry-Perot cavity experiments with vertical-cavity regenerative amplifiers [83] and photorefractive crystals [84,85]. For a BEC in a cavity, in addition to the three atomic motional modes with annihilation operators b 0 , b AE for transverse momenta 0, AEℏq c (with q c ¼ 2π=Λ c for the pattern length scale Λ c ), we have also the corresponding intracavity photonic modes with annihilation operators a 0 , a AE . ...
We describe a mechanism for guiding the dynamical evolution of ultracold atomic motional degrees of freedom toward multiparticle entangled Dicke-squeezed states, via nonlinear self-organization under external driving. Two examples of many-body models are investigated. In the first model, the external drive is a temporally oscillating magnetic field leading to self-organization by interatomic scattering. In the second model, the drive is a pump laser leading to transverse self-organization by photon-atom scattering in a ring cavity. We numerically demonstrate the generation of multiparticle entangled states of atomic motion and discuss prospective experimental realizations of the models. For the cavity case, the calculations with adiabatically eliminated photonic sidebands show significant momentum entanglement generation can occur even in the “bad cavity” regime. The results highlight the potential for using self-organization of atomic motion in quantum technological applications.
... However, in these studies there is a striking difference between twowave mixing and four-wave mixing: mean-field models have been derived only for the former [8,9,10,11], never for the latter. In fact, the theory used for interpreting the experimental results obtained with degenerate four-wave mixing photorefractive resonators has always been heuristic [12,13,14,15]. ...
... (1), at order δA i one gets... exactly the same equations as in the UPA, Eqs. (13). In other words: the perturbations of the pump fields do not enter into the linearized evolution of the intracavity modes and the linear stability of the complete model turns out to be the same as that of the UPA model of the previous section. ...
... The results just presented admit a short enunciation: the linearization of the full degenerate four-wave mixing model leads to unphysical predictions. The physical rationale behind this failure is that linearization of the full model leads to the undepleted-pump model (5), see Eqs. (13), as the fluctuations of the pumping fields are not retained by the linearization. Then, as in the UPA model energy is not conserved, at difference with the full model, the non depletion of the pumps leads to an unrealistic high gain for mode A 1 , which is just an artifact due to linearization. ...
We theoretically consider photorefractive degenerate four–wave mixing oscillators and show that, for this particular system, the linear stability analysis technique leads to wrong results. The reason for that astonishing failure lies in the unphysical predictions of the undepleted pump approximation, which appears naturally during the linearization process of the full model. As a consequence, photorefractive four–wave mixing does not admit a perturbative treatment that permits the derivation of mean–field models, and one is forced to use the full model in order to make sensible predictions.
... Here, we focus on the external degrees of freedom and demonstrate numerically the spontaneous generation of Dicke squeezed (DS) states [45] in the atomic motion, by transverse optomechanical self-organization of a Bose-Einstein condensate (BEC) in a laser pumped ring cavity. The ring cavity setup, studied theoretically in [46][47][48] and experimentally in [49,50], is schematically depicted in Fig. 1a). A prolate shaped zero-temperature BEC is placed in an effectively planoplanar ring cavity of effective length L with one lossy and three perfectly reflecting mirrors (κ -cavity photon decay rate), which is pumped by a coherent electric field with pump strength η at frequency ω. ...
We study the transverse optomechanical self-organization of an ultracold bosonic gas in a ring cavity driven by an external laser. By modeling the light-matter interaction with a many-body Hamiltonian, we demonstrate the spontaneous generation of Dicke squeezing and many-particle entanglement of atomic motional states, occurring due to self-organization of photons and atoms in the stripe phase. Once generated, these squeezed states are maintained after a sudden switch-off of the laser pump in a dissipative cavity. Our results highlight the potential of using self-organization of atomic motion as a tool for quantum metrology.
... The pump beams form an angle with respect to the cavity axis and thus are not resonated. Above a given threshold (mainly controlled by the crystal orientation with respect to the pump beams) a fraction of the pumps is scattered towards the cavity axis, giving rise to degenerate FWM emission, characterized by the bistability between two phases separated by p [47][48][49][79][80][81]. A detailed account of the experimental geometry can be found in [79,80]. ...
... Above a given threshold (mainly controlled by the crystal orientation with respect to the pump beams) a fraction of the pumps is scattered towards the cavity axis, giving rise to degenerate FWM emission, characterized by the bistability between two phases separated by p [47][48][49][79][80][81]. A detailed account of the experimental geometry can be found in [79,80]. In order to implement the proposed periodic modulation of the parametric gain, one of the pump beams was reflected by a piezo-mirror before impinging the photorefractive crystal. ...
The periodic modulation of an oscillator's frequency can lead to so-called parametric oscillations at half the driving frequency, which display bistability between two states whose phases differ by \pi. Such phase-locking bistability is at the root of the extraordinary importance of parametric oscillation (and amplification) both in fundamental and applied scenarios. Here we put forward a universal method for exciting tetrastability in parametrically-driven systems, which consists in modulating the amplitude of the parametric drive in such a way that its sign alternates periodically in time. This way, multistability can emerge between four states whose phases differ by a multiple of \pi/2. We prove theoretically the validity of the method, both analytically and numerically, and demonstrate it experimentally in an optical oscillator. The method could be relevant to the fields of pattern formation, (quantum) information processing and simulation, metrology and sensing.
... More results concerning temporal rocking can be found in [30][31][32], as well as more details on the nonlinear dynamics of the system. In fact the nonlinear dynamics of photorefractive oscillators have been studied by different research groups in the past, and we refer the reader to some of the original references (see [33--53]). ...
In the article we explain in detail how to build a photorefractive oscillator (PRO), which is a laser-pumped nonlinear optical cavity containing a photorefractive crystal. The specific PRO whose construction we describe systematically, is based on a Fabry-Perot optical cavity working in a non-degenerate four wave-mixing configuration. This particular PRO has the property that the generated beam exhibits laser-like phase invariance and, as an application, we show how a suitably modulated injected beam converts the output field from phase-invariant into phase-bistable. While the emphasis is made on the making of the experimental device and on the way measurements are implemented, some introduction to the photorefractive effect as well as to the necessary concepts of nonlinear dynamics are also given, so that the article is reasonably self-contained.
... These points are scattered, especially for weak injections, as we are showing the results of different scans. We attribute this scattering to the fact that, in the experiment, the cavity length was not actively stabilized [14], which could have led to slight variations in the cavity resonance from run to run, especially when the lapse between runs was longer than a few minutes. In any case, for a given run, bistable phase locking was observed between a left point and a right point, which are those marked in the figure. ...
We report experimental evidence of bistable phase locking in nonlinear optics, in particular, in a photorefractive oscillator emitting in few transverse modes. Bistable phase locking is a recently proposed method for converting a laserlike system, which is phase invariant, into a phase-bistable one by injecting a suitable spatially modulated monochromatic beam, resonant with the laser emission, into the optical cavity. We experimentally demonstrate that the emission on the fundamental TEM00 mode becomes phase bistable by injection of a beam with the shape of the TEM10 mode with appropriate frequency, in accordance with recent theoretical predictions [ K. Staliunas et al. Phys. Rev. A 80 025801 (2009)]. The experimental observations are supported by an analytical study of a few-transverse-mode photorefractive oscillator model.
... El dispositivo experimental que utilizamos es un oscilador fotorrefractivo que contiene un cristal de BaTiO 3 y que es bombeado por uno (o dos) haces láser provenientes de un láser de Nd-YAG doblado emitiendo a 532 nm, véase laFig. 4 [25]. Este oscilador puede funcionar tanto en configuración de mezcla de dos ondas como en configuración de mezcla de cuatro ondas, tanto degenerada como no, dependiendo de si se usa una cavidad lineal (de tipo Fabry-Perot) o una cavidad en anillo y también de cuántos haces bombean el cristal no lineal. ...
In this article we review the main research activities of the Quantum and Nonlinear Optics group at the Universitat de València in Spain. The main efforts are on the generation of multimode squeezing within nonlinear optical cavities, on the quantum optics side, and on cavity soliton generation, on the nonlinear optics side. However other topics such as quantum walks or soliton formation in Bose-Einstein condensates, among others, are also covered.
... El dispositivo experimental que utilizamos es un oscilador fotorrefractivo que contiene un cristal de BaTiO 3 y que es bombeado por uno (o dos) haces láser provenientes de un láser de Nd-YAG doblado emitiendo a 532 nm, véase laFig. 4 [25]. Este oscilador puede funcionar tanto en configuración de mezcla de dos ondas como en configuración de mezcla de cuatro ondas, tanto degenerada como no, dependiendo de si se usa una cavidad lineal (de tipo Fabry-Perot) o una cavidad en anillo y también de cuántos haces bombean el cristal no lineal. ...
RESUMEN: Revisamos en este artículo la principales actividades investigadoras del grupo de Óptica Cuántica y No Lineal de la Universitat de València (España). Los esfuerzos principales se centran en la generación de luz comprimida multimodo, por lo que respecta a la óptica cuántica, y en la generación de solitones de cavidad en la parte de óptica no lineal. Sin embargo, también se cubren temáticas tales como los paseos cuánticos y la formación de solitones en condensados de Bose Einstein, entre otros. ABSTRACT: In this article we review the main research activities of the Quantum and Nonlinear Optics group at the Universitat de València in Spain. The main efforts are on the generation of multimode squeezing within nonlinear optical cavities, on the quantum optics side, and on cavity soliton generation, on the nonlinear optics side. However other topics such as quantum walks or soliton formation in Bose-Einstein condensates, among others, are also covered.
... Equation (1) can be considered as a minimal model describing (qualitatively) the dynamics of Degenerate Four-Wave Mixing Photorefractive Oscillators (D4PRO), which is the system we have studied. In a D4PRO a photorefractive crystal (BaTiO 3 in our case) is placed within a linear cavity and is pumped by two counter-propagating, coherent pump beams [3,4]. In such case the parametric gain parameter γ in (1) comes from the four-wave mixing process and can be roughly identified with the product of the two pump beams amplitudes. ...
We present preliminary theoretical and experimental results indicating that a high Fresnel number nonlinear optical oscillator with planar mirrors can display four-phase multistability, eventually leading to four-phase patterns. Such situation is similar to that emerging in extended oscillatory systems forced within a 4:1 resonance and, to the best of our knowledge, has not been predicted nor observed previously in an optical system. The fact that rocking (the forcing of a nonlinear oscillator around its natural frequency -1:1 resonance- with an amplitude modulated periodic signal) is able to transform phase invariant systems into phase bistable ones suggests that a similar forcing, applied now to an already phase bistable system, could lead to four-phase multistability. Here we explore such possibility both theoretically and experimentally.
Continuously pumped passive nonlinear cavities can be harnessed for the creation of novel optical frequency combs. While most research activities have focused on third-order 'Kerr' nonlinear interactions, recent studies have shown that frequency comb formation can also occur via second-order nonlinear effects. Here, we extend the study of such quadratic combs to optical parametric oscillator (OPO) configurations, demonstrating that optical frequency combs can be generated in a continuously pumped OPO, in the parametric region around half of the pump frequency. We also numerically model the comb formation dynamics using a single time-domain mean field equation, and obtain simulation results that are in good agreement with experimentally observed spectra. Moreover, the analysis of the coherence properties of the simulated spectra shows the existence of correlated and phase-locked combs. Our work paves the way for a new class of frequency comb sources that could enable straightforward access to new spectral regions, such as the mid-infrared, and stimulate novel applications of frequency combs.
