Double Symmetry Breaking Research Articles

Divide and structure: generating and interswitching orthogonal eigenstates of complementary petal beams using a π-shifted Sagnac interferometer.

One of the many facets of structured light are Ferris wheel/petal beams that can be generated by the addition/superposition of two beams with opposite vorticity/orbital angular momentum (OAM). We demonstrate a simple scheme employing a π-shifted Sagnac interferometer (SI) containing a spiral phase plate (SPP) that divides and structures an incoming beam into two azimuthally complementary petal beams representing orthogonal eigenstates. The half-wave plate in the SI can interswitch/route these intensity patterns between the two outputs of the interferometer. The results are interpreted as a double symmetry breaking--that of helicity due to SPP and handedness due to HWP--experienced by counterpropagating beams in the π-shifted SI. In general, for a Laguerre-Gaussian (LG) incoming mode, the SI produces two orthogonal output states, each consisting of a sum or difference of distinct SPP-modified LG modes and resulting in complementary petal beams convoluted with the incoming mode. We also introduce a three-mirror π-shifted SI that can switch on and switch off opposite sign vortices into different SI arms. The scheme can find applications in particle trapping, information transmission/development of communications protocols, and signal processing (i.e.,multiplexing/demultiplexing when using beams with high vorticity/OAM).

Effect of Symmetry Breaking on Plasmonic Coupling in Nanoring Dimers

Breaking the morphological and compositional symmetries of metallic nanoparticle (NP) dimers provides a novel approach to modulate plasmon coupling between the NPs. In this study, we theoretically investigate the effect of symmetry breaking on the plasmonic coupling in morphologically asymmetric Au nanoring-nanodisk (NR-ND) dimer, compositionally heterogeneous Au-Ag nanoring dimer, and compositionally as well as morphologically asymmetric Au-Ag NR-ND heterodimers. It has been found that when the inner radii of symmetrical Au NR dimer is decreased, the scattering spectral intensity of coupled bonding mode and higher-order coupled bonding mode drastically decreases and increases, respectively. Besides, the effect of aspect ratio on the plasmon resonance modes is investigated. Furthermore, with fixed geometric parameters of one NR and by morphing the shape of the other NR into ND through inner radius, we show the generation and modification of a Fano resonance. As a result of introducing morphological and compositional asymmetry separately, single Fano-type spectral feature is observed in the scattering spectra. We demonstrate that the double Fano resonances can be easily achieved in compositionally and morphologically asymmetric heterodimer with double symmetry breaking. These dual modes are caused by the interference of dipolar bright mode (localized LSPR modes) of Ag NP with the quadrupole and hexapole modes (interband transitions) of the Au NP. Finally, at optimum asymmetric heterodimers, we discussed the effect of refractive index on the Fano-type resonance. These new and simple designs provide a novel insight to modulate optical response and the generation of higher-order Fano resonances, which have many potential applications such as in photonics and refractive index sensing.

Higher Order Fano Resonances and Electric Field Enhancements in Disk-Ring Plasmonic Nanostructures with Double Symmetry Breaking

Optical properties of disk-ring plasmonic nanostructures with double symmetry breaking are investigated theoretically. Tunable higher order Fano resonance is achieved, and it is sensitive to the degree of asymmetry of the nanoring, the offset and the dimension of the nanodisk. It is demonstrated that such higher order Fano resonances originate from the destructive interference between the bright mode of the displaced nanodisk and the dark mode of the asymmetric nanoring. By tunning the asymmetry degree of the nanoring, the offset, and the dimension of the nanodisk, certain higher order Fano resonances can be suppressed or enhanced. Double asymmetry breaking also allows the realization of the stronger electric field enhancement, resulting from the stronger interaction between the displaced nanodisk and the asymmetric nanoring.

Double Symmetry Breaking of Modes in Dual-Core Rotating System

We study spontaneous symmetry breaking in a dual-core system with a rotating double well potential in self-focusing nonlinearity. By tuning the coupling parameter and total optical power, four types of mode have been found. Double symmetry breaking, which is a combination of the symmetry breaking of the waveform and the optical power distribution, occurs under specific conditions. The numerical simulations show that there are some overlaps among the different stable modes, which have confirmed the coexistence of the modes. It is found that the region where the four stable modes coexist shifts with the variation in the rotating speed, and the corresponding parameters, the coupling parameter and total power, decrease sharply with the increase in the rotating speed.

Double symmetry breaking in TmFe4Ge2 compared to RFe4Ge2 (R=Y, Lu, Er, Ho, Dy) magnetic behaviour

TmFe4Ge2 undergoes a double magneto-elastic first order transition at TN,Tc where the high temperature (HT) tetragonal phase disproportionate into two distinct orthorhombic low temperature (LT) phases with commensurate and incommensurate magnetic wave vectors respectively:P42/mnm(HT)TN,Tc→Cmmmq1=(0,12,0)+Pnnm(q2=(0,qy,0),qy≈2/11(LT)Neutron diffraction shows the relative portions of the LT Cmmm and Pnnm competing phases change linearly with T. The amount of the majority HT phase Pnnm (54% at 30K) decreases linearly to 30% down to 10K in favour of the Cmmm phase that dominates the range 26–1.5K. The Tm moments point along the c-axis in both phases while the Fe moments have canted arrangements. The μTm=3.54(3)μB/atom at 1.5K is strongly reduced below the Tm3+ free ion value gJJ=7μB for the q1 phase. The q2 phase corresponds to a 3D canted sinusoidal arrangement. The results are summarised on a phase diagram and compared to the findings in RFe4Ge2 (R=Y, Lu, Er, Ho, Dy) that are reviewed. The multitude of transition paths occurring in those systems arise from the competing magnetoelastic mechanisms involving the R-crystal field anisotropy, the exchange interactions R–R, R–Fe, Fe–Fe of the two sublattices and their coupling to the lattice strain. The geometrical frustration emerging from the compact tetrahedral Fe arrangement with antiferromagnetic interactions leads to 2D and 3D canted, incommensurate and non-magnetic states. The Cmmm transition is triggered by dominating R–R and R–Fe interactions becoming stronger at LT while the Pnnm phase is promoted by Fe–Fe and R–Fe interactions that prevail at HT. Included is also the magnetic structure of the ferromagnetic impurity phase Fe3Ge.

Double symmetry breaking and two-dimensional quantum phase diagram in spin-boson systems

The quantum ground-state and excitation properties of two independent chains of pseudospins (two-level systems) interacting with the same bosonic field are theoretically investigated. Each chain is coupled to a different quadrature of the field, leading to two independent symmetry breakings for increasing values of the two collective spin-boson interaction constants ${\ensuremath{\Omega}}_{C}$ and ${\ensuremath{\Omega}}_{I}$. A phase diagram is provided in the plane (${\ensuremath{\Omega}}_{C}$,${\ensuremath{\Omega}}_{I}$), with four phases that can be characterized by the complex bosonic coherence of the ground states and can be manipulated via geometric Berry effects. In particular, when ${\ensuremath{\Omega}}_{C}$ and ${\ensuremath{\Omega}}_{I}$ are both larger than two critical values, the fundamental subspace has a fourfold degeneracy. Finite-size properties are shown for both critical and ultrastrong values of ${\ensuremath{\Omega}}_{C}$ and ${\ensuremath{\Omega}}_{I}$. Possible implementations in superconducting quantum circuits are detailed.

Double symmetry breaking of solitons in one-dimensional virtual photonic crystals

We demonstrate that spatial solitons undergo two consecutive spontaneous symmetry breakings (SSBs), with the increase of the total power, in nonlinear photonic crystals (PhCs) built as arrays of alternating linear and nonlinear stripes, in the case when the maxima of the effective refractive index coincide with the minima of the self-focusing coefficient and vice versa (i.e., the corresponding linear and nonlinear periodic potentials are in competition). This setting may be induced, as a virtual PhC, by means of the electromagnetically induced-transparency (EIT) technique, in a uniform optical medium. It may also be realized as a Bose-Einstein condensate (BEC) subject to the action of the combined periodic optical potential and periodically modulated Feshbach resonance. The first SSB happens at the center of a linear stripe, pushing a broad low-power soliton into an adjacent nonlinear stripe and gradually suppressing side peaks in the soliton's shape. Then the soliton restores its symmetry, being pinned to the midpoint of the nonlinear stripe. The second SSB occurs at higher powers, pushing the narrow soliton off the center of the nonlinear channel, while the soliton keeps its internal symmetry. The results are obtained by means of numerical and analytical methods. They may be employed to control switching of light beams by means of the varying power.

Spontaneous Breaking of Spatial and Spin Symmetry in Spinor Condensates

Parametric amplification of quantum fluctuations constitutes a fundamental mechanism for spontaneous symmetry breaking. In our experiments, a spinor condensate acts as a parametric amplifier of spin modes, resulting in a twofold spontaneous breaking of spatial and spin symmetry in the amplified clouds. Our experiments permit a precise analysis of the amplification in specific spatial Bessel-like modes, allowing for the detailed understanding of the double symmetry breaking. On resonances that create vortex-antivortex superpositions, we show that the cylindrical spatial symmetry is spontaneously broken, but phase squeezing prevents spin-symmetry breaking. If, however, nondegenerate spin modes contribute to the amplification, quantum interferences lead to spin-dependent density profiles and hence spontaneously formed patterns in the longitudinal magnetization.

Double symmetry breaking and magnetic transitions in ErFe 4Ge 2

We have revised the T-magnetic phase diagram of the compound ErFe 4Ge 2 based on a recent X-ray powder diffraction study and software development enabling a new approach to this complex situation. Special emphasis is given to the intermediate temperature (IT) range 20 K– T N, T c below the double first-order magneto-elastic transition where the tetragonal high-temperature (HT) phase disproportionates into two distinct orthorhombic phases: P4 2/mnm (HT phase) T N, T c=44 K→ Cmmm (majority low-temperature (LT) phase) q 1 = ( 0 , 1 2 , 0 ) + Pnnm (minority IT Phase) ( q 2=(0, q y , 0), q y ≈2/11). The phase diagram comprises three distinct regions: the HT range T N, T c–293 K where the tetragonal phase P4 2/mnm is stable, the IT range 20 K– T N, where the Cmmm and Pnnm phases coexist in strongly variable proportions and the LT range, 1.5–20 K, where Cmmm prevails. The Pnnm phase reaches its highest concentration (≈33%) around 30 K. We report on the multi-axial amplitude modulated incommensurate magnetic structure of the Pnnm phase with a 2D-canted Fe moment arrangement q 2=(0, q y , 0) and on the coexisting Cmmm 3D-canted magnetic phase with q 1 = ( 0 , 1 2 , 0 ) . The spin reorientation transitions occurring in the Cmmm phase relate to the various structural changes both arising from competing magneto-elastic mechanisms, involving the Er crystal field anisotropy the Er–Er, Er–Fe and Fe–Fe exchange interactions and their coupling to the lattice strain. The Er–Er and Er–Fe interactions are dominating in the LT Cmmm phase while the Fe–Fe and Er–Fe interactions prevail in the Pnnm phase.

The breaking of quantum double symmetries by defect condensation

In this paper, we study the phenomenon of Hopf or more specifically quantum double symmetry breaking. We devise a criterion for this type of symmetry breaking which is more general than the one originally proposed in F.A. Bais, B.J. Schroers, J.K. Slingerland [Broken quantum symmetry and confinement phases in planar physics, Phys. Rev. Lett. 89 (2002) 181601]; Hopf symmetry breaking and confinement in (2+1)-dimensional gauge theory, JHEP 05 (2003) 068], and therefore extends the number of possible breaking patterns that can be described consistently. We start by recalling why the extended symmetry notion of quantum double algebras is an optimal tool when analyzing a wide variety of two-dimensional physical systems including quantum fluids, crystals and liquid crystals. The power of this approach stems from the fact that one may characterize both ordinary and topological modes as representations of a single (generally nonabelian) Hopf symmetry. In principle a full classification of defect mediated as well as ordinary symmetry breaking patterns and subsequent confinement phenomena can be given. The formalism applies equally well to systems exhibiting global, local, internal and/or external (i.e. spatial) symmetries. The subtle differences in interpretation for the various situations are pointed out. We show that the Hopf symmetry breaking formalism reproduces the known results for ordinary (electric) condensates, and we derive formulae for defect (magnetic) condensates which also involve the phenomenon of symmetry restoration. These results are applied in two papers which will be published in parallel [C.J.M. Mathy, F.A. Bais, Nematic phases and the breaking of double symmetries, arXiv:cond-mat/0602109, 2006; F.A. Bais, C.J.M. Mathy, Defect mediated melting and the breaking of quantum double symmetries, arXiv:cond-mat/0602101, 2006].

Nematic phases and the breaking of double symmetries

In this paper, we present a phase classification of (effectively) two-dimensional non-Abelian nematics, obtained using the Hopf symmetry breaking formalism. In this formalism, one exploits the underlying double symmetry which treats both ordinary and topological modes on equal footing, i.e., as representations of a single (non-Abelian) Hopf symmetry. The method introduced in the literature [F.A. Bais, B.J. Schroers, J.K. Slingerland, Broken quantum symmetry and confinement phases in planar physics, Phys. Rev. Lett. 89 (2002) 181601; F.A. Bais, B.J. Schroers, J.K. Slingerland, Hopf symmetry breaking and confinement in (2+1)-dimensional gauge theory, JHEP 05 (2003) 068.] and further developed in a paper published in parallel [F.A. Bais, C.J.M. Mathy, The breaking of quantum double symmetries by defect condensation, 2006, arXiv:cond-mat/0602115.] allows for a full classification of defect mediated as well as ordinary symmetry breaking patterns and a description of the resulting confinement and/or liberation phenomena. After a summary of the formalism, we determine the double symmetries for tetrahedral, octahedral, and icosahedral nematics and their representations. Subsequently the breaking patterns which follow from the formation of admissible defect condensates are analyzed systematically. This leads to a host of new (quantum and classical) nematic phases. Our result consists of a listing of condensates, with the corresponding intermediate residual symmetry algebra T r and the symmetry algebra U characterizing the effective “low energy” theory of surviving unconfined and liberated degrees of freedom in the broken phase. The results suggest that the formalism is applicable to a wide variety of two-dimensional quantum fluids, crystals and liquid crystals.

Defect-mediated melting and the breaking of quantum double symmetries

In this paper, we apply the method of breaking quantum double symmetries to some cases of defect-mediated melting. The formalism allows for a systematic classification of possible defect condensates and the subsequent confinement and/or liberation of other degrees of freedom. We also show that the breaking of a double symmetry may well involve a (partial) restoration of an original symmetry. A detailed analysis of a number of simple but representative examples is given, where we focus on systems with global internal and external (space) symmetries. We start by rephrasing some of the well-known cases involving an Abelian defect condensate, such as the Kosterlitz-Thouless transition and one-dimensional melting, in our language. Then we proceed to the non-Abelian case of a hexagonal crystal, where the hexatic phase is realized if translational defects condense in a particular rotationally invariant state. Other conceivable phases are also described in our framework.