Bose-Einstein Condensates from semiconductor surfaces

Bose-Einstein Condensates from semiconductor surfaces
Quantum reflection of Bose-Einstein Condensates from semiconductor surfaces Mark Fromhold, Robin Scott, Tom Judd

Bose-Einstein Condensates from semiconductor surfaces
Quantum reflection of Bose-Einstein Condensates from semiconductor surfaces Mark Fromhold, Robin Scott, Tom Judd School of Physics and Astronomy

Outline Quantum reflection of a BEC from a planar Si surface

Outline Quantum reflection of a BEC from a planar Si surface
Experiments at MIT (Pasquini, Ketterle)

Experiments at MIT (Pasquini, Ketterle) Analysis of the experiments

Experiments at MIT (Pasquini, Ketterle) Analysis of the experiments Interactions, vortex rings and cloud shape crucial at low v

Experiments at MIT (Pasquini, Ketterle) Analysis of the experiments Interactions, vortex rings and cloud shape crucial at low v Controlling and enhancing the reflection process

Experiments at MIT (Pasquini, Ketterle) Analysis of the experiments Interactions, vortex rings and cloud shape crucial at low v Controlling and enhancing the reflection process By changing the geometry and density of the BECs

Experiments at MIT (Pasquini, Ketterle) Analysis of the experiments Interactions, vortex rings and cloud shape crucial at low v Controlling and enhancing the reflection process By changing the geometry and density of the BECs By patterning the surface on a nm scale

Experiments at MIT (Pasquini, Ketterle) Analysis of the experiments Interactions, vortex rings and cloud shape crucial at low v Controlling and enhancing the reflection process By using pancake-shaped BECs Large, low-density, BECs needed for high reflectivity

Experiments at MIT (Pasquini, Ketterle) Analysis of the experiments Interactions, vortex rings and cloud shape crucial at low v Controlling and enhancing the reflection process By changing the geometry and density of the BECs By patterning the surface on the nm scale

Experiments at MIT (Pasquini, Ketterle) Analysis of the experiments Interactions, vortex rings and cloud shape crucial at low v Controlling and enhancing the reflection process By changing the geometry and density of the BECs By patterning the surface on the nm scale Quantum reflection from micron-scale surface patterns

Experiments at MIT (Pasquini, Ketterle) Analysis of the experiments Interactions, vortex rings and cloud shape crucial at low v Controlling and enhancing the reflection process By changing the geometry and density of the BECs By patterning the surface on a nm scale Quantum reflection from micron-scale surface patterns Using an etched zone plate to make a focussing mirror

Experiments at MIT (Pasquini, Ketterle) Analysis of the experiments Interactions, vortex rings and cloud shape crucial at low v Controlling and enhancing the reflection process By changing the geometry and density of the BECs By patterning the surface on a nm scale Quantum reflection from micron-scale surface patterns Using an etched zone plate to make a focussing mirror Classical reflection from an atom-chip diffraction grating

Outline Bragg reflection of a BEC in an optical lattice
Effect of inter-atomic interactions

Effect of inter-atomic interactions Quantum reflection of a BEC from a planar Si surface Experiments at MIT (Pasquini, Ketterle)

Effect of inter-atomic interactions Quantum reflection of a BEC from a planar Si surface Experiments at MIT (Pasquini, Ketterle) Analysis of the experiments

Effect of inter-atomic interactions Quantum reflection of a BEC from a planar Si surface Experiments at MIT (Pasquini, Ketterle) Analysis of the experiments Interactions, vortex rings and cloud shape crucial at low v

Effect of inter-atomic interactions Quantum reflection of a BEC from a planar Si surface Experiments at MIT (Pasquini, Ketterle) Analysis of the experiments Interactions, vortex rings and cloud shape crucial at low v Controlling and enhancing the reflection process By changing the geometry and density of the BECs

Effect of inter-atomic interactions Quantum reflection of a BEC from a planar Si surface Experiments at MIT (Pasquini, Ketterle) Analysis of the experiments Interactions, vortex rings and cloud shape crucial at low v Controlling and enhancing the reflection process By changing the geometry and density of the BECs By patterning the surface on a nm scale

Effect of inter-atomic interactions Quantum reflection of a BEC from a planar Si surface Experiments at MIT (Pasquini, Ketterle) Analysis of the experiments Interactions, vortex rings and cloud shape crucial at low v Controlling and enhancing the reflection process By changing the geometry and density of the BECs By patterning the surface on a nm scale Quantum reflection from micron-scale surface patterns Using an etched zone plate to make a focussing mirror

Effect of inter-atomic interactions Quantum reflection of a BEC from a planar Si surface Experiments at MIT (Pasquini, Ketterle) Analysis of the experiments Interactions, vortex rings and cloud shape crucial at low v Controlling and enhancing the reflection process By changing the geometry and density of the BECs By patterning the surface on a nm scale Quantum reflection from micron-scale surface patterns Using an etched zone plate to make a focussing mirror Classical reflection from an atom-chip diffraction grating

Using solid surfaces to control BECs
Birkl & Fortagh Laser & Photon. Rev. 1, 1 (2006) Atom chips (cold chips) Current-carrying wires micro- fabricated on a surface Atoms usually trapped m from the surface

Birkl & Fortagh Laser & Photon. Rev. 1, 1 (2006) Atom chips (cold chips) Current-carrying wires micro- fabricated on a surface Atoms usually trapped m from the surface Natural surfaces The intrinsic atom-surface attraction can quantum reflect BECs from silicon Thus shielding cold atoms from the disruptive influence of a room-temperature surface

Optical Lattices In the last 10 years, a new type of artificial crystal, known as an optical lattice has provided unprecedented access to energy band transport processes….

Optical Lattices Provide unprecedented access to energy band transport processes….

Laser standing wave provides a periodic potential and energy band structure for ultra-cold alkali atoms Laser 1 Laser 2 At K temperatures, the alkali atoms move slowly enough for their deBroglie wavelength to extend across several lattice periods

Optical Lattices But, in the last 10 years, a new type of artificial crystal, known as an optical lattice has provided unprecedented access to energy band transport processes ….

Optical Lattices Semiconductor superlattices are excellent tools for studying semiclassical motion through energy bands But, in the last 10 years, a new type of artificial crystal, known as an optical lattice has provided unprecedented access to energy band transport processes…. Laser standing wave provides a periodic potential for ultra-cold atoms, similar to that experienced by electrons in crystals

Electron Ultra-cold atom(s)
Carrier Electron Ultra-cold atom(s) e-

Superlattice Laser standing wave
Environment Superlattice Laser standing wave Carrier Electron Ultra-cold atom(s) e-

Electron Ultra-cold atom(s)
Carrier Electron Ultra-cold atom(s) e- Environment Superlattice Semiconductor surface

Atoms cooled by refrigerators made from light
Slow and cool alkali atoms by hitting them with photons Can attain velocities as low as 1 mm/s

Laser standing wave provides a periodic potential and energy band structure for ultra-cold alkali atoms Laser 1 Laser 2 At K temperatures, the alkali atoms move slowly enough for their deBroglie wavelength to extend across several lattice periods

At µK temperatures, the deBroglie wavelength of an entire alkali atom is ~ 1 µm…

Laser 1 Laser 2 … and therefore spans several periods of an optical lattice formed by a laser standing wave

Laser 1 Laser 2 … and therefore spans several periods of an optical lattice formed by a laser standing wave Consequently, the optical lattice gives rise to an energy band structure for ultracold alkali atoms

In contrast to real crystals…..
Atoms undergo almost no scattering Potential can be switched off at will… …thus providing direct access to band dynamics

Exerting a constant force on a neutral atom
Detuning the two laser beams accelerates the optical lattice relative to the atoms

which can generate Bloch oscillations
In the rest frame of the optical lattice, the atoms experience a constant inertial force, which can generate Bloch oscillations

Direct observation of Bloch oscillations
Ben Dahan et al, Phys. Rev. Lett. 76, 4508 (1996)

Data are for a low-density Caesium gas in which atoms act as single independent objects

Data are for a low-density Caesium gas in which atoms act as single independent objects Bloch oscillations have also been observed for higher-density gases where Bose-Einstein condensation occurs, meaning that millions of atoms act like a single “superatom”

Data are for a low-density Caesium gas in which atoms act as single independent objects Ben Dahan et al, Phys. Rev. Lett. 76, 4508 (1996)

Ability to probe directly energy band dynamics attracted us into the cold atom field, initially to explore analogies with chaotic electron transport in superlattices [Scott et al, Phys. Rev. A. 66, (2002)]

Data are for a low-density Caesium gas in which atoms act as single independent objects Bloch oscillations have also been observed for Bose-Einstein condensates [Morsch et al PRL (2001)], formed at sub-µK temperatures

Bose-Einstein condensates
An ensemble of bosons almost all in the ground state Formed when bosons are cold and dense enough for their de Broglie wavelength to become comparable with their mean separation But not realised until 1995 using alkali atom gases Due to immense technical difficulty of keeping atoms sufficiently far apart to prevent solidification, and cold enough (10 nK to μK) for the deBroglie wavelength to span the gap between them 2001 Nobel Prize in Physics predicted in 1924 Robin – talk could maybe do with a more rigid structure Could introduce 1st two bullet points as current work And last three as work you are proposing to do

Exerting a constant force on a neutral atom
Detuning the two laser beams accelerates the optical lattice relative to the atoms

which can generate Bloch oscillations
In the rest frame of the optical lattice, the atoms experience a constant inertial force, which can generate Bloch oscillations

Data are for a low-density Caesium gas in which atoms act as single independent objects Bloch oscillations have also been observed for Bose-Einstein condensates [Morsch et al PRL (2001)]

Simulation of the Bloch oscillations observed by Morsch et al
PRL (2001) BEC dynamics modelled using time-dependent Gross-Pitaevskii equation

Simulation of the Bloch oscillations observed by Morsch et al
PRL (2001) We observed a different dynamical regime by accelerating the BEC more slowly

Confirmed by experimental collaborators (Arimondo) at Pisa
Scott et al, PRA 69, (2004) Fast Bloch oscillations – BEC acts as a single particle Slow Bloch oscillations – BEC disrupted by mean field

Although optical lattices can be used to simulate condensed matter
Traditionally, actual condensed matter surfaces were the enemy of cold atoms But paradoxically, room-temperature surfaces now useful for manipulating cold atoms

R. Folman et al., Phys. Rev. Lett. 84, 4749 (2000) Fortagh & Zimmermann Rev. Mod. Phys. 79, 235 (2007) Atom chips (cold chips) Current-carrying wires micro- fabricated on a surface Atoms usually trapped m from the surface

R. Folman et al., Phys. Rev. Lett. 84, 4749 (2000) Fortagh & Zimmermann Rev. Mod. Phys. 79, 235 (2007) Atom chips (cold chips) Current-carrying wires micro- fabricated on a surface Atoms usually trapped m from the surface Natural surfaces The intrinsic atom-surface attraction can quantum reflect BECs from silicon Thus shielding cold atoms from the disruptive influence of a room-temperature surface

Motivation for studying quantum reflection
Manipulate BECs using intrinsic surface potential only

Manipulate BECs using intrinsic surface potential only Make atom-optical elements, such as mirrors, lenses and cavities, without the need for external fields

Manipulate BECs using intrinsic surface potential only Make atom-optical elements, such as mirrors, lenses and cavities, without the need for external fields Reflection process probes both atom-surface and atom-atom interactions

Quantum reflection Reverses the direction of motion where there is
no classical turning point It occurs when the potential varies rapidly with position e.g. a potential step Energy x

Quantum reflection Energy x

The potential energy of an atom falls rapidly near a surface
Solid ~3 m Energy x

- + - + Due to mutual polarization of the atom and surface… Solid
The potential energy of an atom falls rapidly near a surface Due to mutual polarization of the atom and surface… Solid + - + - ~3 m Energy x

The potential energy of an atom falls rapidly near a surface Due to mutual polarization of the atom and surface… Solid + - …which creates an intrinsic atom-surface attraction: Casimir-Polder potential + - ~3 m Energy x

The potential energy of an atom falls rapidly near a surface Due to mutual polarization of the atom and surface… Solid + - …which creates an intrinsic atom-surface attraction: Casimir-Polder potential + - ~3 m x

Effect of the Casimir-Polder potential on incident atoms
In a classical picture, no atoms would be reflected Solid ~3 m

In a quantum picture, reflection can occur Solid ~3 m

if the deBroglie wavelength spans rapid potential variation, which requires (a) Low vx (b) Weak atom-surface attraction Solid ~3 m X_0 is approximately 0.1 microns

~3 m It is equivalent to a ball bouncing without ever reaching the floor… or suddenly rolling back up a hill !

Quantum reflection from a Si surface
T. Pasquini et al. Quantum reflection from a Si surface PRL (2004) Silicon wafer Quantum reflection can occur if: ~3 m We assume that atoms which are not reflected are either adsorbed by the Si or scatter inelastically.

Observing quantum reflection
Criteria: (a) Low vx (b) Weak atom-surface attraction only realized in exceptional systems:

Criteria: (a) Low vx (b) Weak atom-surface attraction only realized in exceptional systems: Helium or hydrogen atoms incident on liquid helium Where low mass and weak atom-surface attraction allow quantum reflection to occur at energies ~ kB x 10 mK

Criteria: (a) Low vx (b) Weak atom-surface attraction only realized in exceptional systems: Helium or hydrogen atoms incident on liquid helium Where low mass and weak atom-surface attraction allow quantum reflection to occur at energies ~ kB x 10 mK 2. Reflection of alkali atoms from a solid surface requires incident energy ~ kB x 10 nK First achieved for individual cold atoms grazing the surface [F. Shimizu, PRL 86, 987 (2001)]

Quantum reflection of alkali atoms from a solid
requires incident energy ~ kB x 10 nK

Quantum reflection of alkali atoms from a solid
requires incident energy ~ kB x 10 nK First achieved for individual cold atoms grazing the surface [F. Shimizu, PRL 86, 987 (2001)]

r x Quantum reflection for a BEC T. Pasquini et al.
At normal incidence on a Si surface T. Pasquini et al. PRL (2004) r Silicon wafer x Equipotentials of 3D magnetic trap x = 20 rad s-1 BEC prepared in 3D magnetic trap

Dx Quantum reflection for a BEC T. Pasquini et al.
At normal incidence on a Si surface T. Pasquini et al. PRL (2004) Equilibrium destroyed by shifting origin of the harmonic trap Silicon wafer Dx BEC accelerates towards Si surface & is incident with vx ~ ωxΔx

Experimental image of a BEC
Taken from Containing 300,000 Na atoms at 10 nK 60 μm

Experimental image of a BEC
Taken from Containing 300,000 Na atoms at 10 nK About to impinge on a room-temperature Si surface 60 μm

Quantum reflection Potential energy
Occurs far (few microns) from surface when potential varies rapidly Potential energy

Quantum reflection Occurs far (few microns) from surface when potential varies rapidly To quantify, measure fraction of atoms that are reflected

Quantum reflection from a Si surface: experiment
Pasquini et al. PRL 93, (2004)

Pasquini et al. PRL 93, (2004) At high incident velocities, measured reflection probability agrees well with “single-atom” theory

Need to understand why in order to enhance quantum reflection to values required for new atom optical elements Pasquini et al. PRL 93, (2004) At high incident velocities, measured reflection probability agrees well with “single-atom” theory Below 2 mm/s, measured reflection probability decreases

Decrease in reflection probability accompanied by change in structure of BEC Pasquini et al. PRL 93, (2004) At high incident velocities, measured reflection probability agrees well with “single-atom” theory Below 2 mm/s, measured reflection probability decreases

The appearance of the reflected atom cloud gives us a clue Pasquini et al. PRL 93, (2004)

Pasquini et al. PRL 93, (2004) At high incident velocities, the reflected cloud has the same shape as the incident cloud

Pasquini et al. PRL 93, (2004) For incident velocities < 2 mm/s the reflected cloud is distorted and fragmented

Need to understand the fragmentation and suppress it in order to exploit quantum reflection in new atom optical elements Pasquini et al. PRL 93, (2004) For incident velocities < 2 mm/s the reflected cloud is distorted and fragmented

Solved time-dependent Gross-Pitaevskii equation
Cylindrical co-ordinates For a BEC with rotational symmetry about x-axis r x Density profile in x-r plane

The BEC reflects cleanly: no disruption occurs
Reflection from a Si wall (Casimir-Polder potential) Potential profile High impact velocity: 2.1 mm/s Large displacement The BEC reflects cleanly: no disruption occurs

The BEC becomes disrupted
Reflection from a Si wall (Casimir-Polder potential) Potential profile Low impact velocity: 1.2 mm/s Small displacement The BEC becomes disrupted

HIGH impact velocity (vx = 2.1 mm/s) LOW impact velocity
Wall LOW impact velocity (vx = 1.2 mm/s) Scott, Martin, TMF, Sheard, PRL 95, (2005)

Wall Step LOW impact velocity (vx = 1.2 mm/s) Scott, Martin, TMF, Sheard, PRL 95, (2005)

Wall Step LOW impact velocity (vx = 1.2 mm/s) Si Scott, Martin, TMF, Sheard, PRL 95, (2005)

Fragmentation at low velocities is a generic feature
HIGH impact velocity (vx = 2.1 mm/s) Fragmentation at low velocities is a generic feature of reflection from regions of rapid LOW impact velocity (vx = 1.2 mm/s) potential variation Scott, Martin, TMF, Sheard, PRL 95, (2005)

….and also of Bragg reflection of a BEC in an optical lattice
R.G. Scott, A.M. Martin, S. Bujkiewicz, T.M. Fromhold, N. Malossi, O. Morsch, M. Cristiani, and E. Arimondo, Phys. Rev. A 69, (2004) High lattice acceleration: short reflection time Low lattice acceleration: long reflection time

The BEC becomes disrupted
Reflection from a Si wall (Casimir-Polder potential) Potential profile Low impact velocity: 1.2 mm/s Small displacement The BEC becomes disrupted

Frames from the movie for low incident speed 1.2 mm/s
t = 0 ms

t = 90 ms t = 0 ms Due to the inter-atomic interactions, the high density in the standing wave causes atoms to be pushed into “side-lobes”

t = 122 ms t = 90 ms t = 0 ms The “side-lobes” are pushed back towards the axis of cylindrical symmetry by the trap, producing a soliton

t = 122 ms t = 90 ms t = 143 ms t = 0 ms The soliton decays into two vortex rings At the end of the oscillation the atom cloud has a fragmented appearance

Frames from the movie for low incident speed 1.2 mm/s t = 122 ms
For lobes to form: lobe formation time < reflection time

For lobes to form: lobe formation time < reflection time Radial width Longitudinal width Expansion speed Impact speed <

For lobes to form: lobe formation time < reflection time Radial width Longitudinal width Expansion speed Impact speed < Radial width Impact speed < Longitudinal width x Expansion speed n0½

Frames from the movie t = 0 ms

Frames from the movie t = 90 ms t = 0 ms Due to the inter-atomic interactions, the high density in the standing wave causes atoms to be pushed into “side-lobes”

Frames from the movie t = 122 ms t = 90 ms t = 0 ms The “side-lobes” are pushed back towards the axis of cylindrical symmetry by the trap, producing a soliton

Frames from the movie t = 122 ms t = 90 ms t = 143 ms t = 0 ms The soliton decays into two vortex rings At the end of the oscillation the atom cloud has a fragmented appearance

For lobes to form: lobe formation time < reflection time
Frames from the movie t = 122 ms t = 90 ms t = 143 ms t = 0 ms For lobes to form: lobe formation time < reflection time

Frames from the movie t = 122 ms t = 90 ms t = 143 ms t = 0 ms For lobes to form: lobe formation time < reflection time Radial width Longitudinal width Expansion speed Impact speed <

Frames from the movie t = 122 ms t = 90 ms t = 143 ms t = 0 ms For lobes to form: lobe formation time < reflection time Radial width Longitudinal width Expansion speed Impact speed < Radial width Impact speed < Longitudinal width x Expansion speed n0½

Can we suppress fragmentation by changing
parameters of BEC and/or harmonic trap ? and so enable the surface to act as a high-quality mirror

Simple model predicts fragmentation when
find ~ independent of n0 Impact speed < Longitudinal width x Expansion speed Radial width n0½

Simple model predicts fragmentation when
find ~ independent of n0 Impact speed < Longitudinal width x Expansion speed Radial width n0½ i.e. fragmentation occurs for velocities below a critical value vcrit  n0½ Test simple model by comparing this prediction with numerical simulations

Values of vcrit versus n0 from numerical simulations
Line of gradient 0.5 vcrit  n0½ Low density BECs will not fragment at the low speeds required for high R log-log scale

Can we also suppress fragmentation by changing the shape of the BEC ?
and so enable the surface to act as a high-quality mirror

Expect fragmentation when
Expansion speed Impact speed < Longitudinal width x Radial width

Expect fragmentation when
Expansion speed Impact speed < Longitudinal width x Radial width Aspect ratio is crucial: For pancake-shaped cloud expect fragmentation to onset at lower impact speed

The aspect ratio of the atom cloud is crucial
A pancake-shaped BEC reflects cleanly even for low vx = 1.2 mm/s because reflection is over before sidelobes have time to form

Conversely, for a cigar-shaped cloud….
Radial width Longitudinal width With a high aspect ratio Longitudinal width Impact speed < x Expansion speed Radial width Expect fragmentation even for high impact speeds

Simulation repeated for a cigar-shaped BEC with an impact velocity vx = 2.1 mm/s, for which no disruption was seen in original atom cloud

On quantum reflection side-lobes do indeed form…

At the end of the oscillation the atom cloud contains a vortex ring, and has a fragmented appearance

Fragmentation also occurs for BECs without cylindrical symmetry: 3D calculations
Iso-density surfaces Before

Iso-density surfaces Before Standing wave

Before Standing wave Side-lobes form Iso-density surfaces

Iso-density surfaces Before Standing wave Side-lobes form Vortex rings form

Is fragmentation responsible for the reduced reflection probability observed in experiment at low incident velocities ?

Interactions have no intrinsic effect on R
Theory with inter-atomic interactions Single-particle theory

But in experiment fragmentation may reduce R for two reasons
Produces large tail region of low density Hard to detect Scott et al, Phys. Rev. Lett. 95, (2005); 90, (2003); Phys. Rev. A 74, (2006)

Produces large tail region of low density Hard to detect Simulated absorption image Scott et al, Phys. Rev. Lett. 95, (2005); 90, (2003); Phys. Rev. A 74, (2006)

Produces large tail region of low density Hard to detect Damps centre of mass motion Keeps BEC close to surface Reflection time comparable to lifetime measured when the condensate is trapped near the surface Scott et al, Phys. Rev. Lett. 95, (2005); 90, (2003); Phys. Rev. A 74, (2006)

Does the actual Si surface play a role ?

To calculate R, we considered the attractive Casimir-Polder potential
Solid X_0 is approximately 0.1 microns

Solid and ignored the large repulsive potential at the surface itself X_0 is approximately 0.1 microns

The MIT group modelled the surface potential as an infinite barrier…
∞ Solid ….and considered how this barrier affects a static 1D semi-infinite BEC to its left X_0 is approximately 0.1 microns Pasquini et al, PRL 97, (2006)

∞ Healing length Solid Atom density  mean field potential ….and considered how this barrier affects a static 1D semi-infinite BEC to its left X_0 is approximately 0.1 microns Pasquini et al, PRL 97, (2006)

The mean field “softens” the surface potential
Casimir- Polder X_0 is approximately 0.1 microns Pasquini et al, PRL 97, (2006)

Casimir- Polder Mean field potential X_0 is approximately 0.1 microns Pasquini et al, PRL 97, (2006)

Casimir- Polder Total potential X_0 is approximately 0.1 microns Pasquini et al, PRL 97, (2006)

Calculate R for single atom incident on the potentials
Casimir- Polder Total potential Casimir-Polder X_0 is approximately 0.1 microns

Casimir-Polder Total X_0 is approximately 0.1 microns What causes the dip ?

At high incident velocity, reflection occurs near surface
where Casimir-Polder potential dominates, and mean field has little effect X_0 is approximately 0.1 microns

At lower velocity, reflection occurs further from surface
where mean field softens the total potential, thus reducing R X_0 is approximately 0.1 microns

At very low velocity, reflection occurs far from surface
where mean field potential almost constant so R controlled by Casimir-Polder potential alone Why don’t our calculations of R for a moving BEC, which include mean field potential, reveal this dip ? X_0 is approximately 0.1 microns

The 1D static model greatly overestimates effect of the
mean field potential on R V 1D static mean field potential Mean field potential along centre of a 3D BEC undergoing quantum reflection X_0 is approximately 0.1 microns x Mean field builds more slowly for a moving BEC and is weaker away from centre of a 3D condensate

An alternative explanation for low R values seen in expt.
To attain vx < 1mm/s, trap displacement is smaller than radius of BEC Δx X_0 is approximately 0.1 microns Atoms near leading edge will be lost even before trap displacement sets BEC in motion – giving apparent reduction of R

To attain vx < 1mm/s, trap displacement is smaller than radius of BEC X_0 is approximately 0.1 microns Atoms near leading edge will be lost even before trap displacement sets BEC in motion – giving apparent reduction of R

Technical difficulties?
Low velocities require low trap displacements and close BEC-surface proximity which can produce rapid boiling off of atoms Atomic interactions also cause disruption and increased surface pinning. Again, pancakes can help. For Pasquini 2006 PRL

Calculated reflection probability
Single-particle ? With loses How can we increase R to unity ?

Single-particle Including loses How can we increase R to unity ?

Is fragmentation responsible for the reduced reflection probability observed in experiment at low incident velocities ?

With inter-atomic interactions
Not in theory ! With inter-atomic interactions Single-particle

Why does fragmentation reduce measured reflection probability ?

Produces large tail region of low density Hard to detect Simulated absorption image Scott et al, Phys. Rev. Lett. 95, (2005); 90, (2003); Phys. Rev. A 74, (2006)

Produces large tail region of low density Hard to detect Damps centre of mass motion Keeps BEC close to surface Makes reflection time comparable to lifetime measured when the condensate is trapped near the surface Scott et al, Phys. Rev. Lett. 95, (2005); 90, (2003); Phys. Rev. A 74, (2006)

Another possible contribution to the low R values in expt.
To attain vx < 1mm/s, trap displacement is smaller than radius of BEC Δx X_0 is approximately 0.1 microns Atoms near leading edge will be lost even before trap displacement sets BEC in motion – giving apparent reduction of R

Does the actual Si surface play a role ?

Solid X_0 is approximately 0.1 microns

Solid and ignored the large repulsive potential at the surface itself X_0 is approximately 0.1 microns

∞ Solid ….and considered how this barrier affects a static 1D semi-infinite BEC to its left X_0 is approximately 0.1 microns Pasquini et al, PRL 97, (2006)

∞ Healing length Solid Atom density  mean field potential ….and considered how this barrier affects a static 1D semi-infinite BEC to its left X_0 is approximately 0.1 microns Pasquini et al, PRL 97, (2006)

Casimir- Polder X_0 is approximately 0.1 microns Pasquini et al, PRL 97, (2006)

Casimir- Polder Mean field potential X_0 is approximately 0.1 microns Pasquini et al, PRL 97, (2006)

Casimir- Polder Total potential X_0 is approximately 0.1 microns Pasquini et al, PRL 97, (2006)

Casimir- Polder Total potential Casimir-Polder X_0 is approximately 0.1 microns

Casimir-Polder Total X_0 is approximately 0.1 microns What causes the dip ?

At high incident velocity, reflection occurs near surface
where Casimir-Polder potential dominates, and mean field has little effect X_0 is approximately 0.1 microns

At lower velocity, reflection occurs few µm from surface
where mean field softens the total potential, thus reducing R X_0 is approximately 0.1 microns

At very low velocity, reflection occurs far from surface
where mean field potential almost constant so R controlled by Casimir-Polder potential alone Why don’t our calculations of R for a moving BEC, which include mean field potential, reveal this dip ? X_0 is approximately 0.1 microns

The 1D static model greatly overestimates effect of the
mean field potential on R V 1D static mean field potential Mean field potential along centre of a 3D BEC undergoing quantum reflection X_0 is approximately 0.1 microns x Mean field builds more slowly for a moving BEC and is weaker away from centre of a 3D condensate

Single-particle ? With loses How can we increase R to unity ?

To attain vx < 1mm/s, trap displacement is smaller than radius of BEC X_0 is approximately 0.1 microns Atoms near leading edge will be lost even before trap displacement sets BEC in motion – giving apparent reduction of R

With inter-atomic interactions
Calculated reflection probability Single-particle With inter-atomic interactions

Single-particle < deBroglie wavelength Reflection probabilities up to 0.7 reported by Pasquini et al cond-mat/

Option 1: change the way the atoms are accelerated towards the surface

Trap displacement cannot produce the low speeds required for high R

Trap displacement cannot produce the low speeds required for high R
Alternatively: could release BEC from trap and allow it to fall freely towards the surface But release of mean field energy will increase incident speed

A very low-density BEC falling in microgravity may ensure incident velocity remains low ?
Thus giving high R

Option 2: Weaken the atom-surface attraction

Enhancing quantum reflection by reducing surface density
Single particle picture: R(vx)  exp(- c4½ vx)

Single particle picture: R(vx)  exp(- c4½ vx) C4  surface density Surface

Single particle picture: R(vx)  exp(- c4½ vx) C4  surface density Etched Surface

Pasquini et al, PRL 97, (2006)

Etched surface Pasquini et al, PRL 97, (2006)

Etched surface < deBroglie wavelength Bulk surface Pasquini et al, PRL 97, (2006)

Quantum reflection from etched surface patterns
With feature size in range 1-10 m, comparable with deBroglie wavelength

With feature size in range 1-10 m, comparable with deBroglie wavelength Can diffraction from such patterns be used to manipulate/steer BECs ?

With feature size in range 1-10 m, comparable with deBroglie wavelength Can diffraction from such patterns be used to manipulate/steer BECs ? Quantum reflection from an etched zone plate focuses the BEC without using electric or magnetic fields or complicated curved reflecting mirrors

Fresnel Zone Plate – a brief reminder
Traditionally used to focus electromagnetic waves where conventional lenses do not exist, e.g. X-rays

Traditionally used to focus electromagnetic waves where conventional lenses do not exist, e.g. X-rays Also matter waves: neutrons, 4He atoms

Traditionally used to focus electromagnetic waves where conventional lenses do not exist, e.g. X-rays Also matter waves: neutrons, 4He atoms Waves are focused by diffraction from a grating of alternating transparent and opaque concentric circular rings R0 Rn = R0 √n



 vx  f   1

 1 vx f   

 1 vx f   52 m  Focussing of individual 4He atoms transmitted through a zone plate observed by Carnal et al, PRL (1991) and Doak et al, PRL (1999)

 52 m vx > 400 ms-1 → f ~ 1 m Focussing of individual 4He atoms transmitted through a zone plate observed by Carnal et al, PRL (1991) and Doak et al, PRL (1999)

Focussing of BECs that quantum reflect from a zone plate etched in a Si surface
Cross-section through surface R02 m vx f = h f ~ m

Focussing a BEC by quantum reflection from a zone plate: schematic
Zone plate etched in Si surface BEC

Focussing a BEC by quantum reflection from a zone plate: schematic
Zone plate etched in Si surface BEC Does focussing work when inter-atomic repulsion is taken into account ?

Focussing a BEC by quantum reflection from a zone plate: simulation

Zone plate focussing: Only uses intrinsic surface potential – no external fields

Zone plate focussing: Only uses intrinsic surface potential – no external fields External fields can therefore be used for other purposes – e.g. trapping

Zone plate focussing: Only uses intrinsic surface potential – no external fields External fields can therefore be used for other purposes – e.g. trapping May facilitate isothermal compression, or even cooling, of BECs and the transfer of atoms into chip traps

Focussing a BEC using a transmission zone plate

May be useful for lithography: Defining patterns on surfaces in focal plane Writing conduction channels in near-surface 2DEGs

2.5 Electron density (1015 m-2) x

May be useful for lithography: Defining patterns on surfaces in focal plane Writing conduction channels in near-surface 2DEGs But need a sharp focus: Low-density BEC so interactions don’t oppose focussing

May be useful for lithography: Defining patterns on surfaces in focal plane Writing conduction channels in near-surface 2DEGs But need a sharp focus: Low-density BEC so interactions don’t oppose focussing Large radial width so BEC interacts with fine outer ZP rings

May be useful for lithography: Defining patterns on surfaces in focal plane Writing conduction channels in near-surface 2DEGs But need a sharp focus: Low-density BEC so interactions don’t oppose focussing Large radial width so BEC interacts with fine outer ZP rings Microgravity may help satisfy these criteria ?

We’ve considered diffraction from two types of surface pattern
Passive structures … etched patterns that atoms pass through or quantum reflect from

We’ve considered diffraction from two types of surface pattern
Passive structures … etched patterns that atoms pass through or quantum reflect from 2. Active structures … including classical reflection from diffraction gratings made in Tübingen

An Atom Chip Diffraction Grating
A. Günther et al, PRL (2005); ibid (2007)

Put wires on the chip surface….. A. Günther et al, PRL (2005); ibid (2007)

Run current in alternating directions….. A. Günther et al, PRL (2005); ibid (2007)

Apply an offset magnetic field across the wires…. A. Günther et al, PRL (2005); ibid (2007)

This creates an oscillating potential A. Günther et al, PRL (2005); ibid (2007)

A. Günther et al, PRL (2005); ibid (2007)

Intensity Experiment Position A. Günther et al, PRL (2005); ibid (2007)

Position Intensity Single-atom theory Position A. Günther et al, PRL (2005); ibid (2007)

Intensity Experiment Position Intensity Single-atom theory Position A. Günther et al, PRL (2005); ibid (2007)

Single-atom theory Intensity z (µm) z A. Günther et al, PRL (2005); ibid (2007)

Single-atom theory Intensity With repulsive interactions: diffraction orders merge & interfere z z (µm) A. Günther et al, PRL (2005); ibid (2007)

Single-atom theory Intensity With repulsive interactions z z (µm) Counter-intuitively: repulsive interactions make diffraction pattern narrower by depopulating higher momentum diffraction orders A. Günther et al, PRL (2005); ibid (2007)

Single-atom theory Intensity With repulsive interactions … and finite optical resolution of experiments z z (µm) A. Günther et al, PRL (2005); ibid (2007)

Intensity Experiment … and finite optical resolution of experiments z z (µm) A. Günther et al, PRL (2005); ibid (2007)

Intensity Experiment Position Intensity Interacting theory Position T.E. Judd, R.G. Scott, T.M. Fromhold et al, ArXiv:

Interacting theory Experiment T.E. Judd, R.G. Scott, T.M. Fromhold et al, ArXiv:

Atom-chip Interferometry of BECs
G.B. Jo et al, PRL (2007) Atom chip R.G. Scott, T.E. Judd, and T.M. Fromhold, PRL 100, (2008)

Summary BECs can quantum reflect from a room-temperature surface
Suggests possible applications in atom optics if 1. Avoid fragmentation: low-density pancake-shaped BECs 2. Have high reflection probability: nm-scale etched patterns Micron-scale patterns manipulate BECs without external fields Etched zone plate makes a focussing mirror Isothermal transfer of a BEC into a chip trap ? Similar effects occur when two BECs collide and interfere Scott, Judd, Martin, Fromhold, PRL 90, (2003); PRL 95, (2005); PRL 100, (2008) arXiv: ; arXiv:

Scott, Judd, Martin, Fromhold, PRL 90, (2003); PRL 95, (2005); PRL 100, (2008) arXiv: ; arXiv:

Suggests possible applications in atom optics if Scott, Judd, Martin, Fromhold, PRL 90, (2003); PRL 95, (2005); PRL 100, (2008) arXiv: ; arXiv:

Suggests possible applications in atom optics if 1. Avoid fragmentation: low-density pancake-shaped BECs 2. Have high reflection probability: low approach speeds Scott, Judd, Martin, Fromhold, PRL 90, (2003); PRL 95, (2005); PRL 100, (2008) arXiv: ; arXiv:

Suggests possible applications in atom optics if 1. Avoid fragmentation: low-density pancake-shaped BECs 2. Have high reflection probability: low approach speeds Micron-scale patterns manipulate BECs without external fields Scott, Judd, Martin, Fromhold, PRL 90, (2003); PRL 95, (2005); PRL 100, (2008) arXiv: ; arXiv:

Suggests possible applications in atom optics if 1. Avoid fragmentation: low-density pancake-shaped BECs 2. Have high reflection probability: low approach speeds Etched zone plate makes a passive focussing mirror Scott, Judd, Martin, Fromhold, PRL 90, (2003); PRL 95, (2005); PRL 100, (2008) arXiv: ; arXiv:

Suggests possible applications in atom optics if 1. Avoid fragmentation: low-density pancake-shaped BECs 2. Have high reflection probability: low approach speeds Etched zone plate makes a passive focussing mirror Transmission focussing for matter-wave lithography ?? Scott, Judd, Martin, Fromhold, PRL 90, (2003); PRL 95, (2005); PRL 100, (2008) arXiv: ; arXiv:

Suggests possible applications in atom optics if 1. Avoid fragmentation: low-density pancake-shaped BECs 2. Have high reflection probability: low approach speeds Etched zone plate makes a passive focussing mirror Transmission focussing for matter-wave lithography ?? Need large, low-density, atom clouds → microgravity ?? Scott, Judd, Martin, Fromhold, PRL 90, (2003); PRL 95, (2005); PRL 100, (2008) arXiv: ; arXiv:

Possible advantages of Quantum Reflection under microgravity ?
BECs are very dilute and large – so interactions will probably cause little disruption during QR Could release BEC from trap and allow it to fall under microgravity onto the surface. Since there is little mean field energy to release, impact speed could be very low – maybe low enough to create a semiconductor container ? As BEC is large it would span many ZP rings – this, combined with low density, could give tight focus ?

Scott, Judd, Martin, Fromhold, PRL 90, (2003); PRL 95, (2005); PRL 100, (2008) arXiv: ; arXiv:

Suggests possible applications in atom optics if Scott, Judd, Martin, Fromhold, PRL 90, (2003); PRL 95, (2005); PRL 100, (2008) arXiv: ; arXiv:

Suggests possible applications in atom optics if 1. Avoid fragmentation: low-density pancake-shaped BECs 2. Have high reflection probability: nm-scale etched patterns Scott, Judd, Martin, Fromhold, PRL 90, (2003); PRL 95, (2005); PRL 100, (2008) arXiv: ; arXiv:

Suggests possible applications in atom optics if 1. Avoid fragmentation: low-density pancake-shaped BECs 2. Have high reflection probability: nm-scale etched patterns Micron-scale patterns can manipulate BECs Scott, Judd, Martin, Fromhold, PRL 90, (2003); PRL 95, (2005); PRL 100, (2008) arXiv: ; arXiv:

Suggests possible applications in atom optics if 1. Avoid fragmentation: low-density pancake-shaped BECs 2. Have high reflection probability: nm-scale etched patterns Micron-scale patterns can manipulate BECs Etched zone plate makes a passive focussing mirror Scott, Judd, Martin, Fromhold, PRL 90, (2003); PRL 95, (2005); PRL 100, (2008) arXiv: ; arXiv:

Suggests possible applications in atom optics if 1. Avoid fragmentation: low-density pancake-shaped BECs 2. Have high reflection probability: nm-scale etched patterns Micron-scale patterns can manipulate BECs Etched zone plate makes a passive focussing mirror Transmission focussing for matter-wave lithography ?? Scott, Judd, Martin, Fromhold, PRL 90, (2003); PRL 95, (2005); PRL 100, (2008) arXiv: ; arXiv:

Suggests possible applications in atom optics if 1. Avoid fragmentation: low-density pancake-shaped BECs 2. Have high reflection probability: nm-scale etched patterns Micron-scale patterns can manipulate BECs Etched zone plate makes a passive focussing mirror Transmission focussing for matter-wave lithography ?? Prospects for hybrid cold-atom/condensed matter systems ? Scott, Judd, Martin, Fromhold, PRL 90, (2003); PRL 95, (2005); PRL 100, (2008) arXiv: ; arXiv:

Suggests possible applications in atom optics if 1. Avoid fragmentation: low-density pancake-shaped BECs 2. Have high reflection probability: nm-scale etched patterns Micron-scale patterns can manipulate BECs Etched zone plate makes a passive focussing mirror Transmission focussing for matter-wave lithography ?? “Active” diffraction gratings on atom chips Scott, Judd, Martin, Fromhold, PRL 90, (2003); PRL 95, (2005); PRL 100, (2008) arXiv: ; arXiv:

Bose-Einstein Condensates from semiconductor surfaces

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