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Quantum computing with naturally trapped sub-nanometre-spaced ions

Rippe, Lars LU (2006)
Abstract (Swedish)
Popular Abstract in Swedish

Kvantdatorer har den unika egenskapen att de kan utföra samma beräkning för många olika startvärden samtidigt. Informationen i en vanlig dator är lagrad i ett minne som består av bitar, som kan ha värdena 1 eller 0. När ett program körs beror slutresultatet av startvärdena hos dessa bitar. Minnet i en kvantdator lagrar istället kvantbitar, som även de kan ha värdena 1 eller 0. Men kvantbitarna kan även befinna sig i ett ``kanske-tillstånd'', en så kallad superposition, där de kanske har värdet 0 och kanske 1. Om några av kvantbitarna i ett kvantdatorminne från början sätts i ett "kanske-tillstånd", utförs alla beräkningar, vilka motsvarar de olika möjliga kombinationerna av "kanske-bitarna",... (More)
Popular Abstract in Swedish

Kvantdatorer har den unika egenskapen att de kan utföra samma beräkning för många olika startvärden samtidigt. Informationen i en vanlig dator är lagrad i ett minne som består av bitar, som kan ha värdena 1 eller 0. När ett program körs beror slutresultatet av startvärdena hos dessa bitar. Minnet i en kvantdator lagrar istället kvantbitar, som även de kan ha värdena 1 eller 0. Men kvantbitarna kan även befinna sig i ett ``kanske-tillstånd'', en så kallad superposition, där de kanske har värdet 0 och kanske 1. Om några av kvantbitarna i ett kvantdatorminne från början sätts i ett "kanske-tillstånd", utförs alla beräkningar, vilka motsvarar de olika möjliga kombinationerna av "kanske-bitarna", samtidigt när programmet körs. När man sedan ser på resultatet av programmet får man slumpvis ett av de möjliga svaren, vilket kan tyckas vara ineffektivt. Det visar sig, emellertid, att vissa problem som tar orimligt lång tid att beräkna med en vanlig dator, kan lösas effektivt av en kvantdator med specialskrivna program.



I detta arbetet har jag jobbat med kvantbitar, som är baserade på joner som hör till gruppen sällsynta jordartsmetaller. Jonerna sitter mycket nära varandra i genomskinliga kristaller. Dessa joner har den ovanliga egenskapen att kunna komma ihåg "kanske-tillståndet" för en kvantbit länge, trots att "kanske-tillstånd" normal sett är mycket kortlivade. Programmen i våra kvantdatorer består av pulser av laserljus, med vilka vi belyser jonerna. Olika joner påverkas av olika frekvenser hos laserljuset, på liknande sätt som en radiomottagare inställd på en kanal bara tar emot den kanalen. Genom att byta frekvens på ljuset kan olika grupper av joner påverkas separat.



I arbetet, som denna avhandling beskiver, har en teknik utvecklats för att med hjälp av ljuspulser plocka bort alla joner inom ett frekvensintervall och sedan lyfta tillbaka joner med bara en välbestämmd frekvens, som skall utgöra en kvantbit i vår kvantdator. Denna kvantbit skiftas sedan mellan värde 1 och 0 upprepade gånger, en så kallad en-bitars grind. Om man upprepar denna procedur för två olika frekvensintervaller, så kan man skapa två kvantbitar. För att kunna skapa kvantgrindar med två bitar, så måste en kvantbit kunna påverka en annan. I vårt fall kan en jon, som tillhör en av kvantbitarna, ändra vilken ljusfrekvens som en annan jon annars skulle ha påverkats av. ändringen kan liknas vid att radions kanalinställning ändras lite, varvid man inte längre kan ta emot radiokanalen. I detta arbete har vi visat detta fenomen.



Det är endast de joner som råkar sitta nära varandra, som har tillräckligt stor påverkan för att kunna användas som kvantbitar. Vi har experimentellt visat hur endast de joner, som påverkas mycket, kan väljas ut. Ovanstående kvantdatorschema fungerar för två kvantbitar, men skall man ha fler kvantbitar blir det för få joner kvar i ett närliggande område som alla påverkar varandra, för att man skall kunna detektera dem. En metod som gör det möjligt att ha fler kvantbitar beskrivs i denna avhandling. I denna metod har man endast en jon per kvantbit och utläsningen sker med hjälp av en speciell utläsningsjon, som har dåliga kvantbitsegenskaper, men är lätt att detektera.



Frekvensen och fasen på de laserpulser som används, till att manipulera jonerna, måste vara mycket stabil. Jag beskriver därför, hur vi har stabiliserat en laser genom att jämföra dess frekvens med frekvensen hos samma typ av joner, som kvantbitarna består av, och sedan korrigera frekvensfelen. (Less)
Abstract
The main aim of this work, was to lay the foundations for the experimental realisation of a quantum mechanical controlled NOT gate in rare-earth-metal-ion-doped crystals.



Small amounts of rare-earth elements, added during the growth of some inorganic crystals, will become substituted into the crystal lattice as trivalent ions. The trivalent rare-earth-metal ions between cerium, with atomic number 58, and ytterbium, with atomic number 70, have a partly filled 4f shell, which does not extend spatially outside the full 5s and 5p shells. The 4f vacancies make electronic inner shell transitions possible between spectroscopic 4f terms. Some of these optical transitions have coherence times of the order of milliseconds, when... (More)
The main aim of this work, was to lay the foundations for the experimental realisation of a quantum mechanical controlled NOT gate in rare-earth-metal-ion-doped crystals.



Small amounts of rare-earth elements, added during the growth of some inorganic crystals, will become substituted into the crystal lattice as trivalent ions. The trivalent rare-earth-metal ions between cerium, with atomic number 58, and ytterbium, with atomic number 70, have a partly filled 4f shell, which does not extend spatially outside the full 5s and 5p shells. The 4f vacancies make electronic inner shell transitions possible between spectroscopic 4f terms. Some of these optical transitions have coherence times of the order of milliseconds, when the crystals are cooled down to ~ 4 K. There are several reasons for these extraordinary coherence times, which are approximately 8 orders of magnitude greater than those typical for electronic transitions in solids. The most important one is the cage-like shield which the outer 5s and 5p shells provide for the 4f electrons. Furthermore, since these ions are naturally trapped inside the crystal lattice there is no Doppler broadening of the line-width. The coherence properties of these optical transitions is one of the features that makes these materials attractive for use as a solid-state platform for quantum computing, using these ions as qubits. Another appealing characteristic is the fact that different ions have different optical resonance frequencies, which means that ions belonging to different qubits, which only have nm separation, can still be addressed separately by using different laser frequencies. Since the inter-ion spacing is so small, it is possible to make two ions interact strongly, although they are well shielded, through a permanent dipole-dipole interaction. This interaction can be turned on and off by switching between two different ways of encoding the qubit, a most useful feature. When the qubit is represented as a superposition between two ground state hyperfine levels, the interaction is turned off. The interaction is turned on selectively by transferring this superposition to the optical transition with a pi-pulse, for the specific ions that are to interact.



This thesis describes how peaks of ions, absorbing on a single transition, residing in spectral pits with no other ions, have been isolated. It is shown how these ions can be coherently transferred between hyperfine levels via the optically excited state, how the interaction between such peaks of ions representing qubits can be turned on and off, and how subgroups of ions with strong interaction can be distilled out. All the work described here has been performed using the ensemble approach.



The ensemble approach will, however, be difficult to scale up to large numbers of qubits. A method employing a single ion in each qubit, using a specialised ion for readout, has therefore also been proposed.



The rare-earth-metal-ion-based quantum computing experiments require a laser with coherence properties which at least match those of the material. To this end a frequency stabilisation system was developed for a dye laser. This system uses a transient spectral hole in a rare-earth-metal-ion-doped crystal, of the same kind that is used in the experiments, as frequency reference, and is to the authors knowledge the first demonstration of locking a dye laser to a spectral hole. This system provides a line-width of 1 kHz on a 10 microseconds timescale and a frequency drift below 1 kHz/s. (Less)
Please use this url to cite or link to this publication:
author
supervisor
opponent
  • Professor, dr Schmidt-Kaler, Ferdinand, Quanteninformationsverarbeitung, Universität Ulm, Ulm, Tyskland
organization
publishing date
type
Thesis
publication status
published
subject
keywords
Laserteknik, Laser technology, Atom- och molekylärfysik, Atomic and molecular physics, akustik, optik, Elektromagnetism, optics, acoustics, Electromagnetism, Fysik, Physics, entanglement, spectroscopy, rare-earth-metal-ion-doped crystals spectral hole-burning, inversion, excitation, laser stabilization, quantum computation, quantum gate
pages
214 pages
publisher
Division of Atomic Physics, Department of Physics, Faculty of Engineering, LTH, Lund University
defense location
Sal B, Fysiska Institutionen, Sölvegatan 14 Lund.
defense date
2006-12-15 13:15
ISSN
0281-2762
ISBN
978-91-628-6907-6
language
English
LU publication?
yes
id
622d17eb-6ae3-4f7a-9d03-6990be1d9965 (old id 541527)
date added to LUP
2007-10-01 09:28:24
date last changed
2018-11-21 20:36:11
@phdthesis{622d17eb-6ae3-4f7a-9d03-6990be1d9965,
  abstract     = {The main aim of this work, was to lay the foundations for the experimental realisation of a quantum mechanical controlled NOT gate in rare-earth-metal-ion-doped crystals.<br/><br>
<br/><br>
Small amounts of rare-earth elements, added during the growth of some inorganic crystals, will become substituted into the crystal lattice as trivalent ions. The trivalent rare-earth-metal ions between cerium, with atomic number 58, and ytterbium, with atomic number 70, have a partly filled 4f shell, which does not extend spatially outside the full 5s and 5p shells. The 4f vacancies make electronic inner shell transitions possible between spectroscopic 4f terms. Some of these optical transitions have coherence times of the order of milliseconds, when the crystals are cooled down to ~ 4 K. There are several reasons for these extraordinary coherence times, which are approximately 8 orders of magnitude greater than those typical for electronic transitions in solids. The most important one is the cage-like shield which the outer 5s and 5p shells provide for the 4f electrons. Furthermore, since these ions are naturally trapped inside the crystal lattice there is no Doppler broadening of the line-width. The coherence properties of these optical transitions is one of the features that makes these materials attractive for use as a solid-state platform for quantum computing, using these ions as qubits. Another appealing characteristic is the fact that different ions have different optical resonance frequencies, which means that ions belonging to different qubits, which only have nm separation, can still be addressed separately by using different laser frequencies. Since the inter-ion spacing is so small, it is possible to make two ions interact strongly, although they are well shielded, through a permanent dipole-dipole interaction. This interaction can be turned on and off by switching between two different ways of encoding the qubit, a most useful feature. When the qubit is represented as a superposition between two ground state hyperfine levels, the interaction is turned off. The interaction is turned on selectively by transferring this superposition to the optical transition with a pi-pulse, for the specific ions that are to interact.<br/><br>
<br/><br>
This thesis describes how peaks of ions, absorbing on a single transition, residing in spectral pits with no other ions, have been isolated. It is shown how these ions can be coherently transferred between hyperfine levels via the optically excited state, how the interaction between such peaks of ions representing qubits can be turned on and off, and how subgroups of ions with strong interaction can be distilled out. All the work described here has been performed using the ensemble approach.<br/><br>
<br/><br>
The ensemble approach will, however, be difficult to scale up to large numbers of qubits. A method employing a single ion in each qubit, using a specialised ion for readout, has therefore also been proposed.<br/><br>
<br/><br>
The rare-earth-metal-ion-based quantum computing experiments require a laser with coherence properties which at least match those of the material. To this end a frequency stabilisation system was developed for a dye laser. This system uses a transient spectral hole in a rare-earth-metal-ion-doped crystal, of the same kind that is used in the experiments, as frequency reference, and is to the authors knowledge the first demonstration of locking a dye laser to a spectral hole. This system provides a line-width of 1 kHz on a 10 microseconds timescale and a frequency drift below 1 kHz/s.},
  author       = {Rippe, Lars},
  isbn         = {978-91-628-6907-6},
  issn         = {0281-2762},
  keyword      = {Laserteknik,Laser technology,Atom- och molekylärfysik,Atomic and molecular physics,akustik,optik,Elektromagnetism,optics,acoustics,Electromagnetism,Fysik,Physics,entanglement,spectroscopy,rare-earth-metal-ion-doped crystals spectral hole-burning,inversion,excitation,laser stabilization,quantum computation,quantum gate},
  language     = {eng},
  pages        = {214},
  publisher    = {Division of Atomic Physics, Department of Physics, Faculty of Engineering, LTH, Lund University},
  school       = {Lund University},
  title        = {Quantum computing with naturally trapped sub-nanometre-spaced ions},
  year         = {2006},
}