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We demonstrate theoretically that analogues of D-branes in string theory can be realized in rotating, phase-separated, two-component
Bose-Einstein condensates and that they are observable using current experimental techniques. This study raises the possibility
of simulating D-branes in the laboratory.
KeywordsSigma Models-Solitons Monopoles and In...
Contexts in source publication
Context 1
... note that the intriguing experiment that mimicked the brane- antibrane annihilation was performed by Anderson et al. [30]. They created the configuration shown in Fig 3, where the nodal plane of a dark soliton in one component was filled with the other component. By selectively re- moving the filling component with a resonant laser beam, they made a planer dark-soliton in a single-component BEC. ...
Context 2
... our context, this experiment demonstrated the brane-antibrane collision and subsequent creation of cos- mic strings, where the snake instability may correspond to "tachyon condensation" in string theory [31]. The procedure that removes the filling component can de- crease the distance R between two domain walls and cause their collision [see Fig.3]. The tachyon condensa- tion can leave lower dimensional topological defects after the annihilation of D-brane and anti-D-brane. ...
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Citations
... Such interfaces were first discussed in the context of domain walls in the early universe [1][2][3], where they may form the termination points of cosmic strings [4], and later in brane models in superstring theory [5][6][7]. They appear universally across many areas of physics, from the A−B phase boundary in superfluid liquid 3 He [8][9][10][11][12][13], via atomic Bose-Einstein condensates (BECs) [14][15][16][17][18][19], to quantum chromodynamics [20][21][22]. The different order-parameter symmetries imply that the bulk medium on either side of the interface supports different families of topological defects and textures, which therefore cannot cross the interface unchanged. ...
... We choose to work in the three-component limit with ζ ±1 = 0, resulting FIG. 2. Spin-singlet duo and trio amplitudes |A 20 | 2 (a) and |A 30 | 2 (b), obtained in Eqs. (15) and (16) as functions of the interpolating parameter η and the relative phase difference χ . Along χ ≈ 0, η interpolates between the UN and BN phases. ...
... Hence, we can study the behavior of Eqs. (15) and (16) in the parameter space (χ, η), where χ = χ 2 + χ −2 − 2χ 0 , as shown in Fig. 2. First consider χ = 0. We then notice from the variation of |A 30 | 2 in Fig. 2(b) that instead of a monotonic growth from the minimum |A 30 | 2 = 0 (BN), to |A 30 | 2 = 1 (UN), the BN phase reappears around η = 0.5. If instead χ = π , the C phase arises in the vicinity of η = 0, where |A 20 | 2 = 0, |A 30 | 2 = 2 and the spinor (14) coincides with Eq. (9). ...
We systematically and analytically construct a set of spinor wave functions representing defects and textures that continuously penetrate interfaces between coexisting, topologically distinct magnetic phases in a spin-2 Bose-Einstein condensate. These include singular and nonsingular vortices carrying mass or spin circulation that connect across interfaces between biaxial- and uniaxial nematic, cyclic and ferromagnetic phases, as well as vortices terminating as monopoles on the interface (“boojums”). The biaxial-nematic and cyclic phases exhibit discrete polytope symmetries featuring non-Abelian vortices and we investigate a pair of noncommuting line defects within the context of a topological interface. By numerical simulations, we characterize the emergence of nontrivial defect core structures, including the formation of composite defects. Our results demonstrate the potential of spin-2 Bose-Einstein condensates as experimentally accessible platforms for exploring interface physics, offering a wealth of combinations of continuous and discrete symmetries.
... It is also possible to consider even more elaborate and exotic excitations, such as skyrmions in two dimensions (2D) [70] and 3D [71][72][73][74][75], which arise as a spatially varying spin deformation of the ground state of spinor systems as well as knots that are characterized in terms of the Hopf invariant, a topological charge unique to these excitations [76][77][78]. Multicomponent systems also host exotic composite topological excitations such as D-brane solitons-vortices ending on a domain wall [79][80][81]. Thus multicomponent superfluids provide an ongoing resource for topology, facilitating the creation of these exotic excitations in a stable and controlled environment. ...
We explore the effect of using two-dimensional matter-wave vortices to confine an ensemble of bosonic quantum impurities. This is modeled theoretically using a mass-imbalanced homogeneous two-component Gross-Pitaevskii equation where each component has independent atom numbers and equal atomic masses. By changing the mass imbalance of our system we find that the shape of the vortices is deformed even at modest imbalances, leading to barrel-shaped vortices, which we quantify using a multicomponent variational approach. The energy of impurity carrying vortex pairs is computed, revealing a mass-dependent energy splitting. We then compute the excited states of the impurity, which we in turn use to construct “covalent bonds” for vortex pairs. Our work opens a route to simulating synthetic chemical reactions with superfluid systems.
... The vortex-core regions in our experiment thus contain atoms in the nonrotating polar phase, described on this basis by (0, 1, 0) T , as shown in Fig. 1. These exhibit a coherent, stable topological interface between the two distinct magnetic phases 35,36,43 , where the magnetic phase changes continuously within the vortex core. Analogous topological interfaces are universal across many areas of physics, ranging from superfluid liquid 3 He 44,45 to early-universe cosmology and superstring theory 46,47 , as well as to exotic superconductivity 48 . ...
Quantized vortices appear in physical systems from superfluids and superconductors to liquid crystals and high energy physics. Unlike their scalar cousins, superfluids with complex internal structure can exhibit rich dynamics of decay and even fractional vorticity. Here, we experimentally and theoretically explore the creation and time evolution of vortex lines in the polar magnetic phase of a trapped spin-1 87Rb Bose–Einstein condensate. A process of phase-imprinting a nonsingular vortex, its decay into a pair of singular spinor vortices, and a rapid exchange of magnetic phases creates a pair of three-dimensional, singular singly-quantized vortex lines with core regions that are filled with atoms in the ferromagnetic phase. Atomic interactions guide the subsequent vortex dynamics, leading to core structures that suggest the decay of the singly-quantized vortices into half-quantum vortices. Superfluid vortices are important in many diverse systems, including spinor Bose-Einstein condensates. Here, the experimental and theoretical analysis of the creation and time evolution of vortices in the polar phase of a spin-1 Bose-Einstein condensate is presented, showing the evolution of single-quantum vortices towards half-quantum ones.
... It is also possible to consider even more elaborate and exotic excitations, such as skyrmions in 2D [71] and 3D [72][73][74][75][76] which arise as a spatially varying spin deformation of the ground state of spinor systems as well as knots that are characterized in terms of the Hopf invariant, a topological charge unique to these excitations [77][78][79]. Multi-component systems also host exotic composite topological excitations such as D-brane solitonsvortices ending on a domain wall [80][81][82]. Thus, multicomponent superfluids provide an ongoing resource for topology, facilitating the creation of these exotic excitations in a stable and controlled environment. ...
We explore the effect of using two-dimensional matter-wave vortices to confine an ensemble of bosonic quantum impurities. This is modelled theoretically using a mass-imbalanced homogeneous two component Gross-Pitaevskii equation. By changing the mass imbalance of our system we find the shape of the vortices are deformed even at modest imbalances, leading to `barrel' shaped vortices; which we quantify using a multi-component variational approach. The energy of impurity carrying vortex pairs are computed, revealing a mass-dependent energy splitting. We then compute the excited states of the impurity, which we in turn use to construct `covalent bonds' for vortex pairs, leading to the prediction of impurity mediated bound states. Our work opens a new route to simulating synthetic chemical reactions with superfluid systems.
... [37,38,62,63,65,66,83,89]. It should be important to study how the coexistence of the 1 S 0 and 3 P 2 superfluids affects the properties of quantized vortices; since two condensates coexist, vortices will become fractionally quantized and vortices in different condensates weakly repel each other, as the case of miscible two-component BECs [101,102]. It is also known that the vortices may terminate on a domain wall forming a so-called D-brane soliton, which exists in two-component BEC [103][104][105][106] and supersymmetric field theory [107,108], where the end point of the vortex is called a boojum. There is another possibility that a domain wall may terminate on a vortex; a vortex may be attached by a domain wall, as axion strings. ...
In neutron star matter, there exist $^{1}S_{0}$ superfluids in lower density in the crust while $^{3}P_{2}$ superfluids are believed to exist at higher density deep inside the core. In the latter, depending on the temperature and magnetic field, either uniaxial nematic (UN) phase, D$_{2}$-biaxial nematic (D$_{2}$-BN) phase, or D$_{4}$-biaxial nematic (D$_{4}$-BN) phase appears. In this paper, we discuss a mixture of the $^{1}S_{0}$ and $^{3}P_{2}$ superfluids and find their coexistence. Adopting the loop expansion and the weak-coupling approximation for the interaction between two neutrons, we obtain the Ginzburg-Landau (GL) free energy in which both of the $^{1}S_{0}$ and $^{3}P_{2}$ condensates are taken into account by including the coupling terms between them. We analyze the GL free energy and obtain the phase diagram for the temperature and magnetic field. We find that the $^{1}S_{0}$ superfluid excludes the $^{3}P_{2}$ superfluid completely in the absence of magnetic field, they can coexist for weak magnetic fields, and the $^{1}S_{0}$ superfluid is expelled by the $^{3}P_{2}$ superfluid at strong magnetic fields, thereby proving the robustness of $^{3}P_{2}$ superfluid against the magnetic field. We further show that the D$_{4}$-BN phase covers the whole region of the $^{3}P_{2}$ superfluidity as a result of the coupling term, in contrast to the case of a pure $^{3}P_{2}$ superfluid studied before in which the D$_{4}$-BN phase is realized only under strong magnetic fields. Thus, the D$_{4}$-BN phase is topologically most interesting phase, e.g., admitting half-quantized non-Abelian vortices relevant not only in magnetars but also in ordinary neutron stars.
... How these vortices interact with domain walls is an important question. Also, vortices may terminate on a domain wall with forming so-called a D-brane soliton, which is known to exist in two-component Bose-Einstein condensates [101][102][103][104] and supersymmetric field theory [105,106], where the endpoint of the vortex is called as a boojum. Another possibility is that a domain wall may terminate on a vortex, or in other words, a vortex is attached by a domain wall, as axion strings. ...
We work out domain walls in neutron $^{3}P_{2}$ superfluids realized in the core of neutron stars. Adopting the Ginzburg-Landau theory as a bosonic low-energy effective theory, we consider configurations of domain walls interpolating ground states, i.e., the uniaxial nematic (UN), D$_{2}$-biaxial nematic (D$_{2}$-BN), and D$_{4}$-biaxial nematic (D$_{4}$-BN) phases in the presence of zero, small and large magnetic fields, respectively. We solve the Euler-Lagrange equation from the GL free energy density, and calculate surface energy densities of the domain walls. We find that one extra Nambu-Goldstone mode is localized in the vicinity of a domain wall in the UN phase while a U(1) symmetry restores in the vicinity of one type of domain wall in the D$_{2}$-BN phase and all domain walls in the D$_{4}$-BN phase. Considering a pile of domain walls in the neutron stars, we find that the most stable configurations are domain walls perpendicular to the magnetic fields piled up in the direction along the magnetic fields in the D$_{2}$-BN and D$_{4}$-BN phases. We estimate the energy released from the deconstruction of the domain walls in the edge of a neutron star, and show that it can reach an astrophysical scale such as glitches in neutron stars.
... The BEC-Skyrme model also admits a domain wall interpolating between the two vacua. Vortices can terminate on the domain wall, just like in two-component BECs [19,[26][27][28] (see also Ref. [29]). This configuration resembles a D-brane in string theory, thereby called a D-brane soliton [30][31][32][33]. ...
We consider the BEC Skyrme model, which is based on a Skyrme-type model with a potential motivated by Bose-Einstein condensates (BECs), and, in particular, we study the Skyrmions in proximity of a domain wall that inhabits the theory. The theory turns out to have a rich flora of Skyrmion solutions that manifest themselves as twisted vortex rings or vortons in the bulk and vortex handles attached to the domain wall. The latter are linked open vortex strings. We further study the interaction between the domain wall and the Skyrmion and between the vortex handles themselves as well as between the vortex handle and the vortex ring in the bulk. We find that the domain wall provides a large binding energy for the solitons and it is energetically preferred to stay as close to the domain wall as possible; other configurations sticking into the bulk are metastable. We find that the most stable 2-Skyrmion is a torus-shaped braided string junction ending on the domain wall, which is produced by a collision of two vortex handles on the wall, but there is also a metastable configuration that is a doubly twisted vortex handle produced by a collision of a vortex handle on the wall and a vortex ring from the bulk.
... Vortices can terminate on the domain wall, just like in two-component BECs [19,[26][27][28]. ...
We consider the BEC-Skyrme model which is based on a Skyrme-type model with a potential motivated by Bose-Einstein condensates (BECs) and, in particular, we study the Skyrmions in proximity of a domain wall that inhabits the theory. The theory turns out to have a rich flora of Skyrmion solutions that manifest themselves as twisted vortex rings or vortons in the bulk and vortex handles attached to the domain wall. The latter are linked open vortex strings. We further study the interaction between the domain wall and the Skyrmion and between the vortex handles themselves as well as between the vortex handle and the vortex ring in the bulk. We find that the domain wall provides a large binding energy for the solitons and it is energetically preferred to stay as close to the domain wall as possible; other configurations sticking into the bulk are metastable. We find that the most stable 2-Skyrmion is a torus-shaped braided string junction ending on the domain wall, which is produced by a collision of two vortex handles on the wall, but there is also a metastable configuration which is a doubly twisted vortex handle produced by a collision of a vortex handle on the wall and a vortex ring from the bulk.
... In Refs. [1,2], the comparison between dark solitons and D-branes has been made quantitatively. The authors studied a two-component BEC model, and found the energy of this system is the same as the one in a four-dimensional N = 2 supersymmetric sigma model [3]. ...
In this paper we discuss the boson/vortex duality by mapping the (3+1)D Gross–Pitaevskii theory into an effective string theory in the presence of boundaries. Via the effective string theory, we find the Seiberg–Witten map between the commutative and the noncommutative tachyon field theories, and consequently identify their soliton solutions with D-branes in the effective string theory. We perform various checks of the duality map and the identification of soliton solutions. This new insight between the Gross–Pitaevskii theory and the effective string theory explains the similarity of these two systems at quantitative level.
... For instance, analogues of cosmic strings in superfluids [7,8] and analogues of Dirac monopoles in the spin-1 BEC [9,10] have been proposed. 3 He A-B interfaces and the boundary surface of the two-component BEC have been suggested as analogues of branes in string theory [11][12][13]. Isolated monopoles [14] and Dirac monopoles [15] have been observed in recent spin-1 BEC experiments. ...
We propose a boson-vortex duality in 3+1 dimensions for open vortex lines together with planar dark solitons to which the endpoints of vortex lines are attached. Combining the one-form gauge field living on the soliton plane which couples to the endpoints of vortex lines and the two-form gauge field which couples to vortex lines, we obtain a gauge-invariant dual action of open vortex lines with their endpoints attached to dark solitons. We demonstrate numerically the existence of such stationary composite topological excitations in scalar Bose-Einstein condensates. Dynamically stable states of this type are found at low values of the chemical potential in channeled condensates, where the long-wavelength instability of dark solitons is prevented. Our results are reported for parameters typical of current experiments, and open up a way to explore the interplay of different topological structures in scalar Bose-Einstein condensations.
