What

is a Quantumbit?

PD Dr. Kilian Singer

Universität Mainz

www.quantenbit.de/#/teach/Public%20Outreach/

start

Overview

• Classical information processing

• Quantum information processing

• Scalable quantum information processing

Overview

Classical information processing

• Quantum information processing

• Scalable quantum information processing

What is a Bit ?

• Bit is smallest classical information carrier: 0 or 1

– e.g.: TTL 0Volt, 5 Volt

Combination of Bits with Gattes => Computer

NOT NAND

74LS00

With this you can build an universal computer!

Try it:http://www.nand2tetris.org/

How do you build a gate? NAND

74LS00

With this you can build an universal computer!

Try it:http://www.nand2tetris.org/

Relais in Z1 Zuse (1938)

Through miniaturization from

the Bit to the computer

6 01.08.2013

Vaccum tube computer Collosus (1944)

Transistor Computer IBM 7090(1959) First micro chip byJack Kilby (1958)

Overview

Classical information processing

Quantum information processing

• Scalable quantum information processing

What is a quantumbit ?

What is quantummechanics?

What is classical mechanics?

Newton mechanics Bdescribes the movement of one particle

Newton’s law

Trampoline?

Newton mechanics describes movement of plantsn

Quantum mechanics describes the movement of a small particle

Questions:

• Where do the spectral lines come from?

• Why are they at these wavelength?

• Why does the electron not fall into the atom core?

(as moved charge transmits electromagnetical radiation)

Bohr’s atom modell Niels Bohr (1913)

Centrifugal force=Coloumb force

Coulomb potential => Coloumb force

Questions:

Where do the spectral lines come from?

• Why are they at these wavelength?

• Why does the electron not fall into the atom core?

(as moved charge transmits electromagnetical radiation)

Interference with lightwaves

Interference with lightwaves

Complex numbers

(for first semesters)

• Application

– Electronics

– Quantum mechanic

– Fractals: e.g. Mandelbrot:

fractals.bat

Complex numbers

• Solution of equation

• Imaginary number i:

• General complex number:

Complex numbers

• Solution of equation

• Imaginary number i:

• General complex number:

Euler’s formula

What is the relation between ex and

sin(x) & cos(z) ?

Taylor series:

Taylor series also work for complex numbers:

Maxima-File

http://maxima.sourceforge.net/

What is light? Photo effect

(1905 Albert Einstein)

Existency of photons with energy

Short wavelength

UV light

Alcali metal

electrode

Monochromatic

light

Quarz window

Do single photons interfere?

DeBroglie (1929)

Wave character of particles

Bohr’s atom model

Multiples of the DeBroglie-wave length have to fit on

circumference

Questions:

Where do the spectral lines come from?

Why are they at these wavelength?

• Why does the electron not fall into the atom core?

(as moved charge transmits electromagnetical radiation)

Why does the electron not fall

into the atom core?

Schrödinger equation

(1926)

Erwin Schrödinger

http://vergil.chemistry.gatech.edu/notes/quantrev/node8.html

Schrödinger’s equation

http://vergil.chemistry.gatech.edu/notes/quantrev/node8.html

Schrödinger’s equation

http://vergil.chemistry.gatech.edu/notes/quantrev/node8.html

Schrödinger’s equation

http://vergil.chemistry.gatech.edu/notes/quantrev/node8.html

Schrödinger’s equation

http://vergil.chemistry.gatech.edu/notes/quantrev/node8.html

Schrödinger’s equation

http://vergil.chemistry.gatech.edu/notes/quantrev/node8.html

Schrödinger’s equation

http://vergil.chemistry.gatech.edu/notes/quantrev/node8.html

Schrödinger’s equation

http://vergil.chemistry.gatech.edu/notes/quantrev/node8.html

Schrödinger’s equation

http://vergil.chemistry.gatech.edu/notes/quantrev/node8.html

Schrödinger’s equation

http://vergil.chemistry.gatech.edu/notes/quantrev/node8.html

Schrödinger’s equation

http://vergil.chemistry.gatech.edu/notes/quantrev/node8.html

Schrödinger’s equation

http://vergil.chemistry.gatech.edu/notes/quantrev/node8.html

Interpretation

Probability density in analogy

to the light intensity:

Quantized Energy levels as a

consequence of boundary conditions

1d

2dbox

2dcirc

2dharmonic

coulomb

1dbox

http://www.falstad.com/mathphysics.html

Quantized Energy levels as a

consequence of boundary conditions

What is a quantumbit ?

• QBit is smallest quantunmechanical information

carrier:

What is a quantumbit ?

• QBit is smallest quantunmechanical information

carrier:

• Mathematical representation with vectors:

Measurement 50%

50%

Through lower temperatures

from quantum bits to quantum computers Nuclear spins in

silicon

Molecular

NMR

photons nanomechanical

oscillators superconducting

qubits Rydberg

atoms

Atoms

in optical

dipol traps

Trapped ions

Atoms

in cavities

Quantum dots NV color centers

Quantum bits

Temperature scales

Anders Celsius

(1701- 1744)

Daniel Fahrenheit

(1686 – 1736)

William Thomson

Baron Kelvin

(1824 – 1907)

Absolute temperature scale:

Atoms and molecules at rest: 0 °K = - 273,15 °C

Melting point of ice: 0 °C = 273,15 °K

Evaporation point of water: 100 °C = = 373,15 °K

Gas thermometer

pressure p and volume V increase

with increasing temperature T

N : Amount of gas molecules in mol

kB : Boltzmann‘s constant 1,38 · 10−23 J/K

Boyle-Mariotte‘s law

p . V = N . kB . T

What happens at T=0 ???

Interessante Effekte bei Tiefen

Temperaturen

• Supraconductivity

• Suprafluidity

• Nuclear magnetic resonance

tomography

• Quantumcomputing

…

Movie to supraconductivity

Movie to suprafluidity

What is the lowest temperature

reached?

Inner core of sun: 15 000 000 K

Human: 300 K

Cold atoms: 0.000 000 001 K

Doppler cooling

Optical molasses

Magnetic trap

Magneto-optical trap

Magneto-optical trap

Sisyphus cooling

Nobelprice1997 (Chu, Cohen-Tannoudji, Phillips)

Bose Einstein condensate

Bose Einstein condensate

Nobelprice 2001 (Wieman, Ketterle, Cornell)

Bose Einstein condensate: Matter-wave interference

with macroscopic wavefunction

Atom-Laser

Thermal cloud ….. Bose-condensate

Linear Paul trap

Wolfgang Paul

(Nobel price1989)

RF RF

DC

DC

Harmonic Oscillator

Linear Paul Trap: Axial Confinement

(DC potential)

In the ground state:

Lineare Paul-Trap: radial confinement

by Wolfgang Lange

P1/2

S1/2

t = 7 ns

397 nm

Doppler cooling D5/2

t = 1 s

Energ

y

Level scheme of Calcium+

866 nm Repumping

Doppler Cooling

Atom at Rest

n Laser frequency as seen by atom

Doppler Cooling

Moving atom

n Laser frequency as seen by atom

Doppler Cooling

n Laser frequency as seen by atom

Laser cooled ion crystall

Mainz, 40Ca+