We study the dynamics of Bose-Einstein condensates in time-dependent microtraps for the purpose of understanding the influence of the mean field interaction on the performance of interferometers. We identify conditions where the non-linearity due to atom interactions increases the sensitivity of interferometers to a phase shift. This feature is connected with the adiabatic generation of a dark soliton. We analyze the robustness of this phenomenon with respect to thermal fluctuations, due to excited near fields in an electromagnetic surface trap.
For the first time a method for realizing macroscopic quantum optical solitons is presented. Simultaneous photon-number and momentum squeezing is predicted using soliton propagation in an interferometer. Extraction of soliton pulses closer to true quantum solitons than their coherent counterparts from mode-locked lasers is possible. Moreover, it is a general method of reducing photon-number fluctuations below the shot-noise level for non-soliton pulses as well. It is anticipated that similar reductions in particle fluctuations could occur for other forms of interfering bosonic fields whenever …
A new scheme for generating amplitude squeezed light by means of soliton self-phase modulation is experimentally demonstrated. By injecting 180-fs pulses into an equivalent Mach-Zehnder fiber interferometer, a maximum noise reduction of $4.4 \pm 0.3$ dB is obtained ($6.3 \pm 0.6$ dB when corrected for losses). The dependence of noise reduction on the interferometer splitting ratio and fiber length is studied in detail.
By considering matter wave bright solitons from weakly coupled Bose-Einstein condensates trapped in a double-well potential, we study the formation of macroscopic non-classical states, including Schrödinger-cat superposition states and maximally path entangled $N00N$-states. With these macroscopic states, we examine Mach-Zehnder interferometer in the context of parity measurements, in order to obtain Heisenberg limit accuracy for linear phase shift measurement. We reveal that the ratio between two-body scattering length and intra-well hopping parameter can be measured with the scaling beyond t…
We present two simple designs of matter-wave beam splitters in a trapped Bose-Einstein Condensate (BEC). In our scheme, identical pairs of atomic solitons are produced by an adequate control --- in time and/or space --- of the scattering length. Our analysis is performed by numerical integration of the Gross-Pitaevskii equation and supported by several analytic estimates. Our results show that these devices can be implemented in the frame of current BEC experiments. The system has potential applications for the construction of a soliton interferometer.
We find a set of exact solutions of coherent bright solitons in the quasi-one-dimensional (1D) Bose-Einstein condensate (BEC) trapped in a harmonic potential, by using a Gaussian laser well (barrier) with oscillating position to balance the repulsive (attractive) interatomic interaction. The bright solitons do not deform in propagation and are controlled accurately by the laser driving which resonates with the trapping potential. The solitonic motion is more stable for the repulsive BEC than that of the attractive BEC. The results reveal a different kind of soliton trains compared to that repo…
We theoretically investigate an interferometer composed of four four-wave-mixers by Lie group method. Lie group SU(1,2) characterizes the mode transformations of this kind of interferometer. With vacuum state inputs, the phase sensitivity of SU(1,2) interferometer achieves the Heisenberg limit, and the absolute accuracy beats SU(1,1) interferometer because of higher intensity of light inside the interferometer. For different input cases, the optimal combination of output photon number for detection to obtain the best phase sensitivity is calculated. Our research on SU(1,2) interferometer sheds…
We numerically study the classical and quantum dynamics of an atomic bright soliton in a highly-elongated one-dimensional harmonic trap with a Gaussian barrier. In the regime of the recent experiment by Dyke {\it et al.}, the system realizes a coherent nonlinear soliton beam-splitter and interferometer whose accuracy we analyze. In the case of tighter radial trap confinement and enhanced quantum fluctuations, a split soliton can represent a spin-squeezed, or alternatively, a fragmented condensate with reduced phase-coherence that can be measured by interfering the split soliton by the barrier.…
Various phase shifters and absorbers can be put into the arms of a double loop neutron interferometer. The mean intensity levels of the forward and diffracted beams behind an empty four plate interferometer of this type have been calculated. It is shown that the intensities in the forward and diffracted direction can be made equal using certain absorbers. In this case the interferometer can be regarded as a 50/50 beam splitter. Furthermore the visibilities of single and double loop interferometers are compared to each other by varying the transmission in the first loop using different absorber…
Presented is a study of a spin-2 Bose-Einstein condensate (BEC) by unitary quantum simulations of time-dependent soliton-soliton scattering. The quantum simulation method is based on a quantum lattice algorithm which is designed for implementation on a future digital quantum computer but is tested today using a parallel computing architecture based on graphical processing units (GPUs). We analytically solve the spin-2 BEC equations of motion, a nonlinear system of 5 coupled Gross-Pitiaevskii (GP) equations, in one- and two-spatial dimensions. In 1D there are 16 bright soliton and 16 dark solit…
We propose a new interferometer technique for high precision phase measurements such as those in gravitational wave detection. The technique utilizes a pair of optically coupled resonators that provides identical resonance conditions for the upper as well the lower phase modulation signal sidebands. This symmetry significantly reduces the noise spectral density in a wide frequency band compared with single sideband recycling topologies of current and planned gravitational wave detectors. Furthermore the application of squeezed states of light becomes less demanding.
The bright, dark and grey solitons are well-known soliton solutions of the Gross-Pitaevskii equation for the attractive and repulsive BEC. We consider solitons in the dipolar BEC of the fully polarized particles, speaking of the dipolar BEC we mean both the magnetized BEC and the electrically polarized BEC. We show that these two types of the dipolar BEC reveal different behavior of the collective excitations. This is related to the fact that the electric and the magnetic fields satisfy to the different pairs of the Maxwell equation set. Thus we consider them independently. We obtain exact ana…
We suggest a method for creating bright matter solitons by loading a BEC of atoms in a driven tilted optical lattice. It is shown that one can realize the self-focussing regime for the wave-packet dynamics by properly adjusting the phase of the driving field with respect to the phase of Bloch oscillations. If atom-atom interactions are larger than some critical value $g_{min}$, this self-focussing regime is followed by the formation of bright solitons. Increasing the interactions above another critical value $g_{max}$ makes this process unstable. Instead of soliton formation one now meets the …
Optical computing devices can be implemented based on controlled generation of soliton trains in single and multicomponent Bose-Einstein condensates (BEC). Our concepts utilize the phenomenon that the frequency of soliton trains in BEC can be governed by changing interactions within the atom cloud. We use this property to store numbers in terms of those frequencies for a short time until observation. The properties of soliton trains can be changed in an intended way by other components of BEC occupying comparable states or via phase engineering. We elucidate in which sense such an additional d…
We study solitary wave propagation in the condensate of a system of hard-core bosons with nearest-neighbor interactions. For this strongly repulsive system, the evolution equation for the condensate order parameter of the system, obtained using spin coherent state averages is different from the usual Gross-Pitaevskii equation (GPE). The system is found to support two kinds of solitons when there is a particle-hole imbalance: a dark soliton that dies out as the velocity approaches the sound velocity, and a new type of soliton which brightens and persists all the way up to the sound velocity, tr…
A new type of quantum entangled interferometer was recently realized that employs parametric amplifiers as the wave splitting and recombination elements. The quantum entanglement stems from the parametric amplifiers, which produce quantum correlated fields for probing the phase change signal in the interferometer. This type of quantum entangled interferometer exhibits some unique properties that are different from traditional beam splitter-based interferometers such as Mach-Zehnder interferometers. Because of these properties, it is superior to the traditional interferometers in many aspects, …
Quantum sensors based on coherent matter-waves are precise measurement devices whose ultimate accuracy is achieved with Bose-Einstein condensates (BEC) in extended free fall. This is ideally realized in microgravity environments such as drop towers, ballistic rockets and space platforms. However, the transition from lab-based BEC machines to robust and mobile sources with comparable performance is a challenging endeavor. Here we report on the realization of a miniaturized setup, generating a flux of $4 \times 10^5$ quantum degenerate $^{87}$Rb atoms every 1.6$\,$s. Ensembles of $1 \times 10^5$…
Symmetry breaking during phase transitions can lead to the formation of topological defects (such as vortex lines in superfluids). However, the usually studied BEC's have the shape of a cigar, a geometry that impedes vortex formation, survival, and detection. I show that, in elongated traps, one can expect the formation of "grey solitons" (long-lived, non-topological "phase defects") as a result of the same mechanism. Their number will rise approximately in proportion to the transition rate. This steep rise is due to the increasing size of the region of the BEC cigar where the phase of the con…
We numerically demonstrate atomic Fabry-Perot resonances for a pulsed interacting Bose-Einstein condensate (BEC) source transmitting through double Gaussian barriers. These resonances are observable for an experimentally-feasible parameter choice, which we determined using a previously-developed analytical model for a plane matter-wave incident on a double rectangular barrier system. By simulating an effective one-dimensional Gross-Pitaevskii equation, we investigate the effect of atom number, scattering length, and BEC momentum width on the resonant transmission peaks. For $^{85}$Rb atomic so…
We propose a new method of creating solitons in elongated Bose-Einstein Condensates (BECs) by sweeping three laser beams through the BEC. If one of the beams is in the first order (TEM10) Hermite-Gaussian mode, its amplitude has a transversal phase slip which can be transferred to the atoms creating a soliton. Using this method it is possible to circumvent the restriction set by the diffraction limit inherent to conventional methods such as phase imprinting. The method allows one to create multicomponent (vector) solitons of the dark-bright form as well as the dark-dark combination. In additio…
Particle-wave duality enables the construction of interferometers for matter waves, which complement optical interferometers in precision measurement devices. This requires the development of atom-optics analogs to beam splitters, phase shifters, and recombiners. Integrating these elements into a single device has been a long-standing goal. Here we demonstrate a full Mach-Zehnder sequence with trapped Bose-Einstein condensates (BECs) confined on an atom chip. Particle interactions in our BEC matter waves lead to a non-linearity, absent in photon optics. We exploit it to generate a non-classica…
We propose a scheme to detect analog Hawking radiation (HR) in an atomic Bose-Einstein condensate (BEC) through measuring the diffusion of a dark soliton. The HR is generated by changing the transverse trapping potential of the BEC to obtain a background flow, which is subsonic in downstream and supersonic in upstream, satisfying the condition of black hole horizon. When the system is in thermal equilibrium at Hawking temperature, a dark soliton is created in the upstream. Due to the influence of the HR, the motion of the dark soliton is similar to a Brownian particle and hence exhibits an app…
Interference results when a quantum particle is free to choose among a few indistinguishable paths. A canonical example of Bohr's complementarity principle [1] is a two-path interferometer with an external detector coupled to one of the paths. Then, interference between the two paths vanishes (i.e. dephasing) if one is able to detect, even in principle, the path taken by the particle. This type of which path (WP) experiment was already executed with photons, cooled atoms, neutrons, solitons, and more recently with electrons in a mesoscopic system [2]. In the latter experiment path determinatio…
In this paper we study dark solitons in quasi-one-dimensional Bose-Einstein condensates (BECs) in presence of an anharmonic external potential. The theoretical model is based on the Muñoz-Mateo and Delgado (MMD) equation that describes cigar-shaped BECs with repulsive interatomic interactions. Since MMD equation presents a nonpolynomial form, the soliton-sound recombination cannot display the same pattern presented in the cubic model. We perform numerical simulations to compare both cases.
We study the statics and dynamics of anisotropic, stable, bright and dark-in-bright dipolar quasi-two-dimensional Bose-Einstein condensate (BEC) solitons on a one-dimensional (1D) optical-lattice (OL) potential. These solitons mobile in a plane perpendicular to the 1D OL trap can have both repulsive and attractive contact interactions. The dark-in-bright solitons are the excited states of the bright solitons. The solitons, when subject to a small perturbation, exhibit sustained breathing oscillation. The dark-in-bright solitons can be created by phase imprinting a bright soliton. At medium vel…
We use stochastic Gross-Pitaevskii equation to study dynamics of Bose-Einstein condensation. We show that cooling into a Bose-Einstein condensate (BEC) can create solitons with density given by the cooling rate and by the critical exponents of the transition. Thus, counting solitons left in its wake should allow one to determine the critical exponents z and nu for a BEC phase transition. The same information can be extracted from two-point correlation functions.
