

Soliton Project: Publications 
Controlled formation and reflection of a bright solitary matterwave

A L Marchant, T P Billam, T P Wiles, M M H Yu, S A Gardiner, S L Cornish

Nature Communications 4, 1865 (2013) arXiv:1301.5759 (2013) 
Solitons are nondispersive wave solutions that arise in a diverse range of nonlinear systems, stablised by a focussing or defocussing nonlinearity. First observed in shallow water, solitons have subsequently been studied in many other fields including nonlinear optics, biophysics, astrophysics, plasma and particle physics. They are characterised by well localised wavepackets that maintain their initial shape and amplitude for all time, even following collisions with other solitons. Here we report the controlled formation of bright solitary matterwaves, the 3D analog to solitons, from BoseEinstein condensates of 85Rb and observe their propagation in an optical waveguide. These results pave the way for new experimental studies of bright solitary matterwave dynamics to elucidate the wealth of existing theoretical work and to explore an array of potential applications including novel interferometric devices, the study of shortrange atomsurface potentials and the realisation of Schrodingercat states.

Bright solitary matter waves: formation, stability and interactions 
Contribution to: Spontaneous Symmetry Breaking, Selftrapping, and Josephson Oscillations (Progress in Optical Science and Photonics)

T P Billam, A L Marchant, S L Cornish, S A Gardiner, N G Parker

arXiv:1209.0560 (2012) 
In recent years, bright solitonlike structures composed of gaseous BoseEinstein condensates have been generated at ultracold temperature. The experimental capacity to precisely engineer the nonlinearity and potential landscape experienced by these solitary waves offers an attractive platform for fundamental study of solitonic structures. The presence of three spatial dimensions and trapping implies that these are strictly distinct objects to the true soliton solutions. Working within the zerotemperature meanfield description, we explore the solutions and stability of bright solitary waves, as well as their interactions. Emphasis is placed on elucidating their similarities and differences to the true bright soliton. The rich behaviour introduced in the bright solitary waves includes the collapse instability and symmetrybreaking collisions. We review the experimental formation and observation of bright solitary matter waves to date, and compare to theoretical predictions. Finally we discuss the current stateoftheart of this area, including beyondmeanfield descriptions, exotic bright solitary waves, and proposals to exploit bright solitary waves in interferometry and as surface probes.

BoseEinstein condensation of ^{85}Rb by direct evaporation in an optical dipole trap

A L Marchant, S Händel, S A Hopkins, T P Wiles and S L Cornish

Phys. Rev. A 85, 053647 (2012) arXiv:1203.6598 
We report a simple method for the creation of BoseEinstein condensates of ^{85}Rb by direct evaporation in a crossed optical dipole trap. The independent control of the trap frequencies and magnetic bias field afforded by the trapping scheme permits full control of the trapped atomic sample, enabling the collision parameters to be easily manipulated to achieve efficient evaporation in the vicinity of the 155 G Feshbach resonance. We produce nearly pure condensates of up to 4x10^{4} atoms and demonstrate the tunable nature of the atomic interactions.

Magnetic transport apparatus for the production of ultracold atomic gases in the vicinity of a dielectric surface

S Händel, A L Marchant, T P Wiles, S A Hopkins and S L Cornish

Rev. Sci. Instrum. 83, 013105 (2012) arXiv:1109.5340 
We present an apparatus designed for studies of atomsurface interactions using quantum degenerate gases of ^{85}Rb and ^{87}Rb in the vicinity of a room temperature dielectric surface. The surface to be investigated is a superpolished face of a glass Dove prism mounted in a glass cell under ultrahigh vacuum (UHV). To maintain excellent optical access to the region surrounding the surface magnetic transport is used to deliver ultracold atoms from a separate vacuum chamber housing the magnetooptical trap (MOT). We present a detailed description of the vacuum apparatus highlighting the novel design features; a low profile MOT chamber and the inclusion of an obstacle in the transport path. We report the characterization and optimization of the magnetic transport around the obstacle, achieving transport efficiencies of 70% with negligible heating. Finally we demonstrate the loading of a hybrid opticalmagnetic trap with ^{87}Rb and the creation of BoseEinstein condensates via forced evaporative cooling close to the dielectric surface.

Guided transport of ultracold gases of rubidium up to a roomtemperature dielectric surface

A L Marchant, S Händel, T P Wiles, S A Hopkins and S L Cornish

New J. Phys. 13, 125003 (2011) arXiv:1108.0316 
We report on the guided transport of an atomic sample along an optical waveguide up to a roomtemperature dielectric surface. The technique exploits a simple hybrid trap consisting of a single beam dipole trap positioned ~125 µm below the field zero of a magnetic quadrupole potential. Transportation is realized by applying a moderate bias field (<12 G) to displace the magnetic field zero of the quadrupole potential along the axis of the dipole trap. We use the technique to demonstrate that atomic gases may be controllably transported over 8 mm with negligible heating or loss. The transport path is completely defined by the optical waveguide and we demonstrate that, by aligning the waveguide through a super polished prism, ultracold atoms may be controllably delivered up to a predetermined region of a surface.

Experiments on ultracold quantum gases of ^{85}Rb and ^{87}Rb

S Händel

Phd Thesis, (University of Durham, Durham UK 2011) 
This thesis describes a new apparatus designed to study ultracold gases of
rubidium. The apparatus comprises a sixbeam MOT chamber and a differential
pumping stage leading into a 'science chamber'. This science chamber
is constructed from a rectangular glass cell. Atomic gases of rubidium are collected
in a MOT and then transferred into a magnetic quadrupole trap. This
quadrupole trap is mounted on a motorised translation stage. This setup
transports the atoms into the science chamber, where they are transferred
into a static quadrupole trap which is built around the glass cell. During
the transport the atoms are deflected over a glass prism, which shields the
science chamber from stray rubidium from the MOT chamber. The magnetic
transport is studied in detail and the deflection over the glass prism is fully
described simulating the displacement of the quadrupole trap.
Using the magnetic quadrupole trap in the science chamber to store one
rubidium isotope, we are able to load the other rubidium isotope in the
MOT chamber and transfer it also into the science chamber. There, the two
magnetic traps are merged and variable ratios of isotopic mixtures can be
created. The merging of the two quadrupole traps could be employed in
future experiments to cool ^{85}Rb sympathetically with ^{87}Rb. In the science
chamber forced radiofrequency evaporation is performed and the loading of
a fardetuned dipole trap is studied. Initially the dipole trap is realised as a
hybrid trap, a single beam dipole trap in combination with the quadrupole
trap. Further studies include the loading of a crossed beam dipole trap. We
demonstrate that the apparatus is capable of producing ^{87}Rb condensates.
Preliminary studies of ^{85}Rb in the dipole trap are included which hopefully
in future will lead to a quantum degenerate gas of ^{85}Rb.

Magnetic merging of ultracold atomic gases of ^{85}Rb and ^{87}Rb

S Händel, T P Wiles, A L Marchant, S A Hopkins, C S Adams and S L Cornish

Phys Rev A 83, 053633 (2011) arXiv:1011.6273 
We report the magnetic merging of ultracold atomic gases of ^{85}Rb and ^{87}Rb by the controlled overlap of two initially spatially separated magnetic traps. We present a detailed analysis of the combined magneticfield potential as the two traps are brought together that predicts a clear optimum trajectory for the merging. We verify this prediction experimentally using ^{85}Rb and find that the final atom number in the merged trap is maximized with minimal heating by following the predicted optimum trajectory. Using the magneticmerging approach allows us to create variableratio isotopic Rb mixtures with a single lasercooling setup by simply storing one isotope in a magnetic trap before jumping the laser frequencies to the transitions necessary to laser cool the second isotope.

Realizing bright matterwave soliton collisions with controlled relative phase

T P Billam, S L Cornish and S A Gardiner

Phys Rev A 83, 041602(R) (2011) arXiv:1010.3219 
We propose a method to split the ground state of an attractively interacting atomic BoseEinstein condensate into two bright solitary waves with controlled relative phase and velocity. We analyze the stability of these waves against their subsequent recollisions at the center of a cylindrically symmetric, prolate harmonic trap as a function of relative phase, velocity, and trap anisotropy. We show that the collisional stability is strongly dependent on relative phase at low velocity, and we identify previously unobserved oscillations in the collisional stability as a function of the trap anisotropy. An experimental implementation of our method would determine the validity of the meanfield description of bright solitary waves and could prove to be an important step toward atom interferometry experiments involving bright solitary waves.

Offresonance laser frequency stabilization using the Faraday effect

A L Marchant, S Händel, T P Wiles, S A Hopkins, C S Adams and S L Cornish

Opt Lett 36, 64 (2011) arXiv:1007.2531 
We present a simple technique for stabilization of a laser frequency off resonance using the Faraday effect in a heated vapor cell with an applied magnetic field. In particular, we demonstrate stabilization of a 780 nm laser detuned up to 14 GHz from the ^{85}Rb D_{2}5^{2}S_{1/2}F=2 to 5^{2}P_{3/2}F'=3 transition. Control of the temperature of the vapor cell and the magnitude of the applied magnetic field allows locking ~614 GHz red and blue detuned from the atomic line. We obtain an rms fluctuation of 7 MHz over 1h without stabilization of the cell temperature or magnetic field.

Bright solitary waves of trapped atomic BoseEinstein condensates 
N.G. Parker, A.M. Martin, C.S. Adams, S.L. Cornish

Physica D 238, 14561461 (2009) arXiv:0802.4275 
Motivated by recent experimental observations, we study theoretically multiple bright solitary waves
of trapped BoseEinstein condensates. Through variational and numerical analyses, we determine the
threshold for collapse of these states. Under piphase differences between adjacent waves, we show that
the experimental states lie consistently at the threshold for collapse, where the corresponding inphase
states are highly unstable. Following the observation of two longlived solitary waves in a trap,weperform
detailed threedimensional simulations which confirm that inphase waves undergo collapse while a
piphase difference preserves the longlived dynamics and gives excellent quantitative agreement with
experiment. Furthermore, intermediate phase differences lead to the growth of population asymmetries
between the waves, which ultimately triggers collapse.

Quantum reflection of bright matterwave solitons 
S.L. Cornish, N.G. Parker, A.M. Martin, T.E. Judd, R.G. Scott, T.M. Fromhold, C.S. Adams

Physica D 238, 12991305 (2009) arXiv:0802.4362 
We propose the use of bright matterwave solitons formed from BoseEinstein condensates with
attractive interactions to probe and study quantum reflection from a solid surface at normal incidence.
We demonstrate that the presence of attractive interatomic interactions leads to a number of advantages
for the study of quantum reflection. The absence of dispersion as the soliton propagates allows precise
control of the velocity normal to the surface and for much lower velocities to be achieved. Numerical
modelling shows that the robust, selftrapped nature of bright solitons leads to a clean reflection from
the surface, limiting the disruption of the density profile and permitting accurate measurements of the
reflection probability.

Collapse times of dipolar BoseEinstein condensates 
C. Ticknor, N.G. Parker, A. Melatos, S.L. Cornish, D.H.J. O'Dell, and A.M. Martin

Phys. Rev. A 78, 061607(R) (2008) arXiv:0809.4294 
We investigate the time taken for global collapse by a dipolar BoseEinstein condensate. Two semianalytical approaches and exact numerical integration of the meanfield dynamics are considered.
The semianalytical approaches are based on a Gaussian ansatz and a ThomasFermi solution for the shape of the condensate. The regimes of validity for these two approaches are determined, and their
predictions for the collapse time revealed and compared with numerical simulations. The dipolar interactions introduce anisotropy into the collapse dynamics and predominantly lead to collapse in the
plane perpendicular to the axis of polarization.

Collisions of bright solitary matter waves 
N.G. Parker, A.M. Martin, S.L. Cornish and C.S. Adams

J. Phys. B 41, 045303 (2008) arXiv:0712.3002 
The collisions of threedimensional bright solitary matter waves formed from atomic BoseEinstein condensates are shown to exhibit rich behaviour. Collisions range from being elastic to completely destructive due to the onset of collapse during the interaction. Through a detailed quantitative analysis we map out the role of relative phase, impact speed and interaction strength. In particular, we identify the importance of the collapse time in the onset of unstable collisions and show how the relative phase controls a population transfer between the waves. Our analysis enables us to interpret recent experimental observations of bright solitary matter waves.

Bright solitary waves and trapped solutions in BoseEinstein condensates with attractive interactions

N.G. Parker, S.L. Cornish, C.S. Adams and A.M. Martin

J. Phys. B 40, 31273142 (2007) arXiv:0705.0064 
We analyse the static solutions of attractive BoseEinstein condensates under transverse confinement, both with and without axial
confinement. By full numerical solution of the GrossPitaevskii equation and variational methods we map out the condensate solutions,
their energetic properties and their critical points for instability. With no axial confinement a bright solitary wave solution will
tend to decay by dispersion unless the interaction energy is close to the critical value for collapse. In contrast, with axial
confinement the only decay mechanism is collapse. The energetic stability of a bright solitary wave solution against decay increases
with higher radial confinement. Finally, we consider the stability of dynamical states containing up to four solitons and find good
agreement with recent experiments.

Formation of Bright MatterWave Solitons during the Collapse of Attractive BoseEinstein Condensates

S.L. Cornish, S.T. Thompson, C.E. Wieman 
Phys. Rev. Lett. 96, 170401 (2006) arXiv:condmat/0601664 
We observe bright matterwave solitons form during the collapse of 85Rb condensates in a threedimensional (3D) magnetic trap.
The collapse is induced by using a Feshbach resonance to suddenly switch the atomic interactions from repulsive to attractive.
Remnant condensates containing several times the critical number of atoms for the onset of instability are observed to survive the collapse.
Under these conditions a highly robust configuration of 3D solitons forms such that each soliton satisfies the condition for stability
and neighboring solitons exhibit repulsive interactions.


