“Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum...

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Atomic Physics “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computing

Transcript of “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum...

Page 1: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

Atomic Physics

“Driving Doppler Down”

Doppler-free methodsLaser cooling, trapping,

quantum computing

Page 2: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

Cool (2.1MB and loads of fun)

This .Zip file includes the .Exe, .Hlp, and .Dll files as well as other supporting files for Visual Basic. Download the .Zip and unzip it. Then, run the Setup.exe program. Enjoy!!

Exsetup Movie (469KB) Here it is!! (after much sweat and conversion) This .AVI shows the experimental setup for laser cooling and trapping. Play it in Cool or on any .AVI movie player

Cold Cesium (130KB) This is a movie shows a cold, dense cloud of cesium atoms created in the laboratory!!

Trap! (257KB) This .AVI shows the Magneto-Optic Trap (MOT). Its starts with optical molasses and then suddenly the magnetic field gradient is applied and the trap forms. The field is turned off and the cloud slowly spreads.

Optical Molasses (129KB) Here is a simulation created using Cool. It demonstrates what "Cool" people call Optical Molasses. Try it out! (or just make your own!)

Dark MOT (161KB) Another simulation which demonstrates a dark magneto-optic trap (MOT). Download this or make your own!

Light MOT (91 KB) Another simulation which demonstrates a light magneto-optic trap (MOT). Download this or make your own!

Light to Dark MOT (243KB) This a simulation that starts as a light MOT then changes to a dark MOT

Dark to Light MOT (252KB) This simulation starts as a dark MOT then changes

COOLING – FUN demos…

Page 3: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

Motion of an atom affects the absorption frequency, and its emission frequency

From kinetic theory, we know the fraction of atoms with velocity between v and v+dv

f(v)dv = {M/(2πkT)}1/2 exp {-Mv2/(2kT)} dv = (1/u√π) exp(-v2/u2) dv

Where u is the most probable velocity u = √(2kT/M)Since the fractional shift in frequency is δ/ω0 = v/cThen the line profile is GDoppler(ω) = (c/(uω0√π)exp {-(c2/u2)(ω – ω0)2/ω0

2}

Question: Estimate the halfwidth at room temperature (a) for Balmer-alpha, (b) for the cesium resonance line

A reminder:

Page 4: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

Example 1: Crossed beams

Doppler broadening depends on the collimation of the 2 beams – generally this is much larger for the atoms – α typically about 10-3 radiansBut also broadening due to the short interaction time – “transit-time broadening”.Typical widths are of the order of 1 MHz for visible spectra.

Page 5: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

“Co-linear” – Saturated Absorption spectroscopy

A laser beam approaching the atoms with a weak intensity, and a wavelength off-resonance by a small amount – the atoms with a certain velocity relative to the laser will be promoted to level 2, “burning a hole” in the Gaussian thermal distribution of level 1 atoms.

Page 6: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

Saturated Absorption spectroscopy

Improvement in “halfwidth” is typically at least 1000, with consequent improvement in precision of measuring the resonance frequency.

Most experiments (a) utilize double-beam

geometries – comparing the difference of the 2 beams –one crossing, the other not-crossing.

(b) And/or chop the pump beam to remove time variations.

Page 7: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

2-photon spectroscopy

Excitation can be to a virtual level, midway between the initial and final state (of opposite parity) – e.g. a 1s to 2s transition in hydrogenLyman-α has a wavelength of 126 nm; hence each of the 2 photons needs a wavelength of 252 nm; each of these produced by frequency –doubling a green line (at 504 nm)

Page 8: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

Two vital factors for precision measurements

1. Measuring frequency directly

2. Cooling the source

Page 9: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

Measuring the wavelength/frequency

A femtosecond laser is so short that its energy distribution can span frequencies from f to 2f – then direct comparisons of different frequency-doubled components (from the doubling crystal) allows measurement of the mode number. The unknown frequency can then be compared with these accurately known absolute frequencies. – to precisions of parts in 1012 to 1014.

Important corollary: Stepping up frequency ranges from a direct lower frequency measurement (say, 109 Hz) to frequencies in the 1014 Hz range

Page 10: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

Laser cooling of atomsPhoton momentum can be used to apply a force to each atom: radiation of intensity I exerts a force on an area A: Frad = IA/cIn the figure, the atom then radiates in all directions so that its momentum long the beam is reduced – i.e. the beam is cooled.

Example: a sodium beam at T=900K (from the oven shown) v0 = 1000m/sAcceleration is a = - (ħk/M) (γ/2) = v(recoil) (γ/2) For sodium τ = 1/ γ = 16 ns, v(recoil) = 3 cm/sHence the stopping distance x = 2v0

2 τ/v(recoil) = 1.1 m

But note - if the velocity changes the resonant wavelength changes – so how do we fix that?

Page 11: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

Use Zeeman splitting to match cooling velocity!! (the first time)

Matching the magnetic field can bring the atom to rest just at the end of the solenoid – such an experiment indicates a concentration of atoms which gradually move away perpendicular to the beam, where no laser cooling has occurred - W. D. Phillips and H. Metcalf, Phys. Rev. Lett. 48, 596-599 (1982).So now let’s do it in all directions… (three are enough) => TRAP

Page 12: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

Tuning the laser slightly below the resonance absorption of a stationary sodium atom. The atom sees the head-on photon as Doppler shifted upward toward its resonant frequency and it is therefore more strongly absorbed than a photon traveling in the opposite direction which is Doppler shifted away from the resonance. For room temperature sodium atom, the incoming photon is Doppler shifted up 0.97 GHz, so to get the head on photon to match the resonant frequency would require that the laser be tuned below the resonant peak by that amount. This method of cooling sodium atoms was proposed by Theodore Hansch and Arthur Schawlow at Stanford University in 1975 and achieved by Chu at AT&T Bell Labs in 1985.

Alternative longitudinal cooling:

Sodium atoms were cooled from a thermal beam at 500K to about 240 mK. The experimental technique involved directing laser beams from opposite directions upon the sample, linearly polarized at 90°with respect to each other. Six lasers could then provide a pair of beams along each coordinate axis. The effectively "viscous" effect of the laser beams in slowing down the atoms was dubbed "optical molasses" by Chu.

Page 13: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

Three-dimensional cooling – optical molasses

The effectivemolasses force(off resonance by kv)

Page 14: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

Another way: Use laser “chirping” to match cooling velocity!!

Vary the laser frequency to match the change in velocity: we must vary the frequency by GHz in milliseconds! – how do we do that?

Electro-optic modulators and rf techniques can do it fast enough – the crystals produce sideband frequencies which can then be varied rapidly by applying an rf signal.

The slower atoms in the distribution have been brought to zero velocity, to give a narrow low velocity peak.

Velocity distribution of“chirped” atoms

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Chirping of a laser

The chirp of an optical pulse is usually understood as the time dependence of its instantaneous frequency. Specifically, an up-chirp (down-chirp) means that the instantaneous frequency rises (decreases) with time.

Example: consider a pulse with a Gaussian envelope and a quadratic temporal phase:

This is associated with a linear chirp, i.e., with a linear variation of the instantaneous frequency: (Fourier transform)

Page 16: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

Magnetic field trap

The “wrongly-connected” Helmholtz coils give zero magnetic field at the center, increasing in all directions away from the center.

Page 17: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

Combination – the MOTAdding the (6) molasses cooling lasers yields an imbalance of the net forces always towards the center.

The physical geometry The Zeeman splitting in the magnetic field.

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Dipole cooling – example: the atomic fountain

An intense laser beam can change the energy levels of an atom (AC Stark shift). If the laser frequency is less than the resonance frequency, this forms a potential well attracting the atoms into a volume of high laser intensity – this is called a “dipole-force” trap which can be loaded with the “molasses cooled” atoms.

This can be produced neatly on a microscopic scale by producing a standing wave, and thus a string of small traps.

After the cold atoms have been trapped, the lasers can be turned off, allowing the atoms to fall – and then be detected lower down by a probe laser…

Page 19: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

The atomic fountain – in principle, and in reality

Page 20: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

The fountain geometry increases the time between the two interrogations by gently tossing the atoms up and letting them fall back down under the influence of gravity, all under high vacuum. Atoms are collected and then launched through a single microwave cavity, which interrogates the atoms both on the way up and again on the way down. The atoms are then detected optically to determine the information about the microwave frequency. This cycle is then repeated. The longer time between interrogations improves the precision of the measurement,.

Page 21: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

Who was Sisyphus?The gods had condemned Sisyphus to ceaselessly rolling a rock to the top of a mountain, whence the stone would fall back of its own weight. They had thought with some reason that there is no more dreadful punishment than futile and hopeless labor.

Sisyphus, being near to death, rashly wanted to test his wife's love. He ordered her to cast his unburied body into the middle of the public square. Sisyphus woke up in the underworld. And there, annoyed by an obedience so contrary to human love, he obtained from Pluto permission to return to earth in order to chastise his wife. But when he had seen again the face of this world, enjoyed water and sun, warm stones and the sea, he no longer wanted to go back to the infernal darkness. Recalls, signs of anger, warnings were of no avail. Many years more he lived facing the curve of the gulf, the sparkling sea, and the smiles of the earth. A decree of the gods was necessary. Mercury came and seized the impudent man by the collar and, snatching him from his joys, led him forcibly back to the underworld, where his rock was ready for him.

Page 22: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

A modern Sisyphus – the atom

Page 23: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

Manipulating atoms, part 1The Ioffe-Pritchard trap adds magnetic fields from coils (much further apart but with the Helmholtz phase) to pinch and “Ioffe” coils which hold the atoms in the center.

By slowly reducing the fields, evaporative cooling can take place –i.e. the hotter atoms jump out of the potential lattice, leaving the cooler atoms.

Such methods can lead to atom temperatures less than 10-9K. There is no theoretical limit – just the number of atoms trapped.

Page 24: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

This photo shows about 1 million ytterbium atoms illuminated by a blue laser in an experimental atomic clock that holds the atoms in a lattice made of intersecting laser beams. The photo was taken with a digital camera through the window of a vacuum chamber. NIST is studying the possible use of ytterbium atoms in next-generation atomic clocks based on optical frequencies, which could be more stable and accurate than today's best time standards, which are based on microwave frequencies.

August 2009: The NIST ytterbium clock is based on about 30,000 heavy metal atoms that are cooled to 15 microkelvins (close to absolute zero) and trapped in a column of several hundred pancake-shaped wells

N.B. The NIST Cs-clock is stable to 1 second in 10,000 years!

TIME

Page 25: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

Manipulating atoms, part 2- to a Bose-Einstein condensate -

As the temperature gets colder, the interatomic interactions will maintain their “collision memory”, leading to coherence in any scattering (and a “coherence time”. The atoms then behave as a single quantum entity. If they are bosons, this can lead to a Bose-Einstein condensation.

The thermal DeBroglie wavelength can be defined as

λ = h (2πMkT)-1/2

When the inter-atomic spacing reaches (about) this value the bosons tend to condense…

when N/V ≈ (λ)-1/3 = 2.6 (λ)-1/3

see Bose-Einstein statistics for more exact formulation…

Page 26: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

Bose-Einstein condensate and Quantum Computing

The atoms then fit into the potential well, with all energy levels filled up to an effective Fermi level.-> well potential example on left.-> picture of cooling “atom blob” below.-> optical density cuts on right.

Quantum computing comes next!

Manipulation of a string or volume of optical traps…. Quantum mechanics allows optical entanglement and further manipulation of phases as well as just populations in each trap.

Page 27: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

The QubitThe qubit is the quantum analogue of the bit, the classical fundamental unit of information. It is a mathematical object with specific properties that can be realized physically in many different ways as an actual physical system. Just as the classical bit has a state (either 0 or 1), a qubit also has a state.

Note: any linear combination (superposition) is physically possible. In general, thus, the physical state of a qubit is the superposition ψ = α |0>+ β |1> (where α and β are complex numbers).

The state of a qubit can be described as a vector in a two-dimensional Hilbert space, a complex vector space .The states |0> and |1> form an orthonormal basis of quantum states for this vector space.

Fundamental theorem quantifying the improved speed of quantum computers (phase information) first formulated in Shor’s algorithm (1994).

Page 28: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

Any general 2-component state can be written

|Ψ> = cos(θ)|0> + eiφsin(θ)|1>,

where the numbers θ and φ define a point on the unit three-dimensional sphere, as shown here. This sphere is often called the Bloch sphere, and it provides a useful means to visualize the state of a single qubit.

Note that the act of measurement yields either the |1> state or the |0> state, but the computer can store much more (an infinite?)amount of information!

This is relevant to the first definition of a“computer” by Alan Turing in 1936.

The Turing machine (1936) was essentially a table of look-up values for any calculation.

For a good history of the development of quantum computing seehttp://plato.stanford.edu/entries/qt-quantcomp/#2.1

Visualizing the Qubit

Page 29: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

Atomic quantum systems in optical micro-structures by T. M¨uther et alAbstract (Journal of Physics: Conference Series 19 (2005) 97–101)

We describe an experiment on evaporative cooling in a far-detuned optical dipole trap for 87Rb. The dipole trap is created by a solid state laser at a wavelength of 1030 nm. To achieve high initial phase space densities allowing for efficient evaporative cooling, we have optimised the loading process from a magneto-optical trap into the dipole trap. These investigations aim at the creation of an ‘all-optical’ BEC based on a simple experimental scheme. As an example, we present the transport of atoms in a ring-shaped guiding structure, i.e. optical storage ring, for cold atoms which is produced by a micro-fabricated ring lens.

Absorption images after 10 ms TOF (left), and measured temperatures (right, in nK) for different laser powers.

Schematic of the ring lens (left) and fluorescence image of the atoms in the storage ring (right)

Page 30: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

Quantum computing differs from classical computing in that a classical computer works by processing “bits” that exist in two states, either one or zero.

Quantum computing uses quantum bits, or qubits, which, in addition to being one or zero can also be in a "superposition," which is both one and zero simultaneously. This is possible because qubits are quantum units like atoms, ions, or photons that operate under the rules of quantum mechanics instead of classical mechanics. The "superposition" state allows a quantum computer to process significantly more information than a classical computer and in a much shorter time.

The area of quantum computing took off about 14 years ago after Peter Shor created a quantum algorithm that could factor large integers much more efficiently than a classical computer. Though researchers are still many years away from creating a quantum computer capable of running the Shor algorithm, progress has been made. Kumar’s group, which uses photons as qubits, found that they can entangle two indistinguishable photons together in an optical fiber very efficiently by using the fiber’s inherent nonlinear response. They also found that no matter how far you separate the two photons in standard transmission fibers they remain entangled and are "mysteriously" connected to each other’s quantum state.

Page 31: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

Science Daily (Dec. 8, 2008) — Physicists have taken a significant step toward creation of quantum networks by establishing a new record for the length of time that quantum information can be stored in and retrieved from an ensemble of very cold atoms. Though the information remains usable for just milliseconds, even that short lifetime should be enough to allow transmission of data from one quantum repeater to another on an optical network.

The new record – 7 milliseconds for rubidium atoms stored in a dipole optical trap – is scheduled to reported December 7 in the online version of the journal Nature Physics by researchers at the Georgia Institute of Technology. The previous record for storage time was 32 microseconds, a difference of more than two orders of magnitude.

2 graduate students at Georgia Tech

Page 32: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

Optical entanglement

Entangled photons remain interconnected even when separated by large distances. Merely observing one instantaneously affects the properties of the other. The entanglement can be used in quantum communication to pass an encryption key that is by its nature completely secure, as any attempt to eavesdrop or intercept the key would be instantly detected!

Example 1 – 2 linearly polarized photons of perpendicular polarizations

See http://www.davidjarvis.ca/entanglement/

Page 33: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

An ultraviolet laser sends a single photon through Beta Barium Borate. As the photon travels through the crystal, there is a chance it will split into 2 photons, each of half the energy (twice the wavelength). If it splits, the photon will exit from the Beta Barium Borate as two photons. The resulting photon pair are entangled!

Result

Example of a photon entangler

Page 34: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

a Bell-state quantum eraser

Consequently, the left-hand slit will receive photons with a counter-clockwise polarization, and the right-hand slit will pass photons with a clockwise polarization. Note: Polarization does not affect interference patterns. Initially, neither detector shows an interference pattern. Since we control the polarization of photons passing through the slits and we know the polarization accepted by each slit, we can deduce which way the photons travelled (counter-clockwise through the left; clockwise through the right). Thus no interference patterns are detected. However, if we rotate the polarizing filter in front of detector A so that the polarizations of the photons that hit the detector are the same (that is, we can no longer distinguish between clockwise and counter-clockwise polarizations), then the interference pattern appears at both detectors! How do the photons arriving at detector B know that the polarizations have been "erased" at detector A?

The Bell-state quantum eraser has one more feature: each slit is covered by a substance that filters the (circular) polarization of a photon.

Page 35: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

Entangled source point-to-point link(information going to “Bob” and “Alice”)

continuousor

pulsed

near IRor

telecom IR

fiber or free-space transmission

phase or polarization qubits

Single-photon or number sensitive

Generation Propagation Detection

Page 36: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

Top: Cross-section scanning tunneling microscope (STM) image shows indium arsenide quantum dot regions embedded in gallium arsenide. Each 'dot' is approximately 30 nanometers long–faint lines are individual rows of atoms. (Color added for clarity.) Bottom: Schematic of NIST-JQI experimental set up. Orienting the resonant laser at a right angle to the quantum dot light minimizes scattering (Credit: Top: J.R. Tucker; Bottom: Solomon/NIST)

Quantum Dots - 1

Quantum dots are nanoscale regions of a semiconductor material similar to the material in computer processors but with special properties due to their tiny dimensions. Though they can be composed of tens of thousands of atoms, quantum dots in many ways behave almost as if they were single atoms. Unfortunately, almost is not good enough when it comes to the fragile world of quantum cryptography and next-generation information technologies. When energized, a quantum dot emits photons, or “particles” of light, just as a solitary atom does. But imperfections in the shape of a quantum dot cause what should be overlapping energy levels to separate. This ruins the delicate balance of the ideal state required to emit entangled photons.

Page 37: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

Two lasers—one shining from above the quantum dot and the other illuminating it from the side—the researchers were able to manipulate energy states in a quantum dot and directly measure its emissions.

Quantum Dots - 2

Andrew Shields at Toshiba and colleagues at the University of Cambridge, produced entangled photons with an efficiency of 70% -- compared to a previous best figure of 49%. The improved performance approaches that required for useful applications, which means that devices emitting entangled light could one day be as common as lasers and light-emitting diodes New J. Physics 8, 29 (2006)

The team produced entangled photons from a crystal just 12 nm in diameter made from indium arsenide embedded within a gallium arsenide and aluminium arsenide cavity. When excited by a laser pulse, the quantum dot captures two electrons and two holes to form a "biexciton" state in the dot. One of the electrons recombines with a hole to create a photon, leaving behind an intermediate "exciton" state in the dot of one electron and one hole. The other electron-hole pair then combines to create a second photon.

Page 38: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

In 1995 teams in Colorado and Massachusetts achieved BEC in super-cold gas. This feat earned those scientists the 2001 Nobel Prize in physics.

S. Bose, 1924

Light

A. Einstein, 1925

Atoms

E. Cornell W. KetterleC. Wieman

Using Rb and Na atoms

In a Bose Einstein Condensate there is a macroscopic number of atoms in the ground state

Page 39: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

When atoms are illuminated by laser beams they feel a force which depends on the laser intensity.

Two counter-propagating beams

Standing wave

)()( 2 kxSinxV

Page 40: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

Perfect Crystals

Mimic electrons in solids: understand

their physics

Quantum Information

Atomic Physics

Page 41: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

• Any processing of information is always performed by physical means

• Bits of information obey laws of classical physics.

Information is physical!

Every 18 months microprocessors double in speed: Faster=Smaller

?

Atoms ~

0.0000000001 mENIAC ~ m

1946 2000

Microchip ~ 0.000001 m

Page 42: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

Computer technology will reach a point where classical physics is no longer a suitable model for the laws of physics. We need quantum mechanics.

Year

Size

Page 43: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

weirdness

Page 44: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

• Fundamental building blocks of classical computers:

• STATE: 0 or 1• Definitely 0 or 1

Bits• Fundamental building blocks

of quantum computers:• STATE: |0� or |1�• Superposition: a |0�+b |1�

Qubits

Page 45: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

• A classical register with n bits can be in one of the 2n

posible states.

• A quantum register can be in a superposition of ALL 2n posible states.

n 2n

2 bits 4 states: 00, 01, 10, 11

3 bits 8 states

10 bits 1024 states

30 bits 1 073 741 824 states

500 bits More than our estimate of the number of atoms in the universe

Page 46: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

A quantum computer can perform 2n operations at the same time due to superposition :

However we get only one answer when we measure the result:

F[000] F[001] F[010] . .

F[111]

Only one answer F[a,b,c]

Page 47: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

• Qubit: Probabilistic |� =a |0�+b |1�

We get either |0� or |1� with corresponding

probabilities |a|2 and |b|2 |a|2+|b|2=1

The measurement changes the state of the qubit!

|� � |0� or |� � |1�

• Classical bit: Deterministic. We can find out if it is in state 0 or 1 and the measurement will not change the state of the bit.

Page 48: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

Strategy: Develop quantum algorithms

Use entanglement: measurement of states can be highly correlated

Use superposition to calculate 2n values of function simultaneously and do not read out the result until a useful outout is expected with reasonably high probability.

Page 49: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

Quantum entanglement: Is a quantum phenomenon in which the quantum states of two or more objects have to be described with reference to each other.

Entanglement Correlation between observable physical properties

e.g. |� =( |0A 0B�+ |1A 1B�)/√2

Product states are not entangled

|� =|0 0�

•“Spooky action at a distance” - A. Einstein

• “ The most fundamental issue in quantum mechanics” –E. Schrödinger

Page 50: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

172475846743 198043

870901

Use mathematical hard problems: factoring a large number

Shared privately with Bob

Page 51: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

• Shor's algorithms (1994) allows solving factoring problems which enables a quantum computer to break public key cryptosystems.

Classical Quantum

172475846743=?x? 172475846743= 870901 x198043

Page 52: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

Neutral atoms

Trapped ions

Electrons in semiconductors

Many others…..

Page 53: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

DiVincenzo criteria

1. Scalable array of well defined qubits.

2. Initialization: ability to prepare one certain state

repeatedly on demand.

3. Universal set of quantum gates: A system in which qubits can be made to evolve as desired.

4. Long relevant decoherence times.

5. Ability to efficiently read out the result.

Page 54: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

|1� |0�a. Internal atomic states

b. Different vibrational levels

|1� |0�

Internal states are well understood: atomic spectroscopy & atomic clocks.

Page 55: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

Scalability: the properties of an optical lattice system do not change when the size of the system is increased.

Page 56: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

• Internal state preparation: putting atoms in the same internal state. Very well understood (optical pumping technique is in use since 1950)

• Motional states preparation: Atoms can be cooled to motional ground states (>95%)

Page 57: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

Only one classical gate (NAND) is needed to compute any function on bits!

Page 58: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

?1. How many gates do we need to make ?

2. Do we need one, two, three, four qubit gates etc?

3. How do we make them?

Answer: We need to be able to make arbitrary single qubit operations and a phase gate

Phase gate:

|0 0�� |00�

|0 1�� |01�

|1 0�� ei |10�

|11� � |11�

a|0�+b|1� c|0�+d|1�X

Page 59: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

Single qubit rotation: Well understood and carried out since 1940’s by using lasers

Laser|0�

|1�

1.

2. Two qubit gate: None currently implemented but conditional logic has been demonstrated

|01 02�

|(01+11)( 02+12)�

|0102+0111+ 1002+1011 �

initial

Combine

Displace

Collision |0102+ei0111+ 1002+1011 �

Page 60: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

Experiment implemented in optical lattices

Page 61: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

Entangled state Environment Classical statistical mixture

Entangled states are very fragile to decoherenceAn important challenge is the design of decoherence resistant entangled states

Main limitation: Light scattering

Page 62: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

Global: Well understood, standard atomic techniques

e.g: Absorption images, fluorescence

Local: Difficult since it is hard to detect one atom without perturbing the other

Experimentally achieved very recently at Harvard: Nature 462 74 (2009).

Page 63: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser

• All five requirements for quantum computations have been implemented in different systems. Trapped ions are leading the way.

• There has been a lot progress, however, there are great challenges ahead……

Overall, quantum computation is certainly a fascinating new field.

Page 64: “Driving Doppler Down” Doppler-free methods Laser cooling, trapping, quantum computinghgberry/delhi2013/atomic-10 - laser traps.pdf · 2013-05-02 · Doppler-free methods Laser