Trapped ions: from Atomic Clocks to Quantum Computers

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Trapped ions from Atomic Clocks to Quantum
Computers
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Basement
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Ion Trappers
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Lab
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LASER
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Ion Trap Vacuum Can
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Ion Trap Electrodes
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Trapped Ions
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What can trapped ions be used for?

• Very pure quantum system
• Measurement of atomic properties
• Isolated from the environment
• Atomic clocks with accuracy of 1 part in a
  billion billion
• Would have lost 0.1s over the lifetime of the
  universe
• Quantum information processing
• Factor numbers in polynomial time!

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Atomic clocks What is the point?

• Navigation
• Communication synchronisation
• Measurement
• Tests of fundamental principles

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What is a clock?

• Oscillator e.g. Pendulum
• Counter e.g. Escapement mechanism

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How good is a clock?

• Quality of an oscillator is defined as the
  frequency of the oscillator divided by the
  uncertainty in the frequency of the oscillator
• Traditional clocks vary
• difficult to compare clocks
• All atoms of a given isotope are identical
• can compare atomic clocks to each other

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Quantum Structure of Atoms

• Electrons in an atom can only exist with certain
  discrete energies
• Transitions between different energy levels have
  precise frequencies
• Transition energies are blurred due to finite
  lifetime of excited states, collisions, ion
  motion, magnetic fields,
• Superposition states can be created where atoms
  are in two states at once (Schrödingers Cat)

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Quantum Structure of Atoms
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Fundamental Principles of Atomic Clocks

• Put the ion into ground state
• Illuminate ion with a tunable source operating
  near the transition frequency
• Detect absorption of the radiation
• Adjust the frequency of the source until it is on
  resonance with the ionic transition

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Frequency

• 1Hz 1 cycle per second - e.g. human pulse
• 10-100Hz - nervous system response time
• 100kHz-10MHz - AM radio
• 100MHz - FM radio
• 1GHz - microwaves
• 100THz-1PHz - IR, visible light, UV

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Resonance
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Ions - what oscillates?

• Atomic clocks make use of quantum mechanical
  superposition states
• The ion is placed in a superposition of two
  internal states
• The phase between the states oscillates with time
• Measuring the state when the ion is in a
  superposition gives a random result

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Ramsey Interferometry
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Atomic clock performance

• Improves as the length of time between the pulses
  increases
• Improves as the frequency of the transition
  increases
• Limited by the need to be able to count the
  cycles of the exciting radiation
• Optical clocks are the present state of the art
• Improves as the ions are cooled
• Improves if entangled ions are used

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Entanglement
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Quantum Computation

• N two-level ions can span a space of dimension 2N
• Can initialise a N-qubit register and perform
  computations on all possible 2N inputs at once
• Quantum algorithms have been designed to make use
  of entanglement during a computation but still
  give a classical result

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My Research

• Need to be able to read out the internal state of
  the ion
• Energy levels used in our implementation are
  separated by a frequency difference much smaller
  than the linewidth of the transitions
• Make use of electromagnetically induced
  transparency (EIT) to cancel absorption from the
  unwanted state

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Results
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Conclusion

• Thank you for your attention
• Further details available at http//nodens.physics
  .ox.ac.uk/mcdonnell/ALsem/
• Any questions?