Simon Thwaite recently completed a D.Phil. in Atomic & Laser Physics at the University of Oxford, and is currently a postdoctoral researcher at the Ludwig Maximilian University in Munich. The first part of his post series commenting on the 2012 Nobel Prize in Physics can be found here.
In this post he gives an overview of the field of trapped ions, describes two of its most important applications, and describes what goes on behind the scenes when a trapped ion interacts with a laser beam.
David J. Wineland – probing trapped atoms with light
David Wineland, an experimental physicist at the National Institute for Standards and Technology (NIST) in Boulder, Colorado, is one of the leading researchers in the field of trapped ions: that is, the study of how positively-charged ions (i.e. atoms stripped of one or more electrons) may be trapped, cooled, and manipulated. This field shares many similarities with experiments on neutral atoms (laser cooling, for example, is just as useful for ions as it is for neutral atoms), but also has a number of significant differences. The most important difference that distinguishes ions from atoms is, obviously enough, the fact that ions have a non-zero net electrical charge. This has two very important consequences.
Trapped ions: trapping and interactions
Applying an electric field to an ion produces a force on the ion: positive ions are drawn in the direction of the field. [In contrast, applying an electric field to a neutral atom changes the ‘shape’ of the atom slightly, since the positively-charged nucleus and negatively-charged electron cloud are drawn in opposite directions, but produces no net force.] Consequently, whereas traps for neutral atoms must rely on combinations of laser light and magnetic fields, ions can be trapped just by electric fields. Most of the recent trapped-ion experiments use some variation on the Paul trap (a.k.a. the quadrupole ion trap) which uses a combination of static (DC) and oscillating (AC) electric fields to trap ions along a 1-dimensional line.
The second important point is that ions interact with one another far more strongly than neutral atoms do: two positive ions repel one another strongly through their mutual Coulomb interaction. [In contrast, neutral atoms typically interact very weakly, and behave essentially like hard spheres: they are ignorant of the presence of one another unless in direct contact.] Consequently, ions held in a Paul trap are subject to two competing tendencies. Firstly, the ions are drawn towards the center of the trap in order to minimize the trapping potential energy; secondly, they strongly repel one another in an attempt to minimize the ion-ion interaction energy. By way of compromise, the ions line up like a string of beads, with inter-ionic distances of the order of a few tens of microns. This is, experimentally speaking, a very convenient state of affairs, since it means that each ion can be individually addressed by a tightly-focused laser beam.
Applications of trapped ions
Strings of laser-cooled ions held in a Paul trap can be put to a variety of uses. One important application lies in the realm of high-precision spectroscopy and frequency standards. Securely trapped, well isolated from the environment, and cooled to a standstill, a single laser-cooled ion in a Paul trap is an ideal subject on which to make precision energy-level measurements (or, equivalently, measurements of the frequency of the electromagnetic radiation that the ion absorbs and emits).
Since frequency is just the inverse of time, a well-defined frequency can be used as a reference point for defining exactly what a ‘second’ is. Single trapped ions thus form an excellent basis for atomic clocks. Such clocks show significantly improved accuracy over those based on the radiation emitted by neutral cesium atoms (the kind which, since 1967, has formed the basis for the SI definition of a second).
A second important application of trapped ions is their use in the field of quantum information processing (a.k.a. quantum computing). This field is founded on the realisation that the laws of quantum mechanics appear to allow for a more powerful model of computation than the (classical) Turing paradigm that underpins computing as we know it. Although this result hasn’t yet been mathematically proven, at this point in time it seems extremely probable that computers that are designed to take advantage of the intricacies of quantum mechanics can efficiently solve problems that are completely intractable for a classical computer.
The best-known example of such a problem is the division of a large integer into its prime factors (e.g. 15 = 3*5; or 70 = 2*5*7) This task is generally believed to be impossible to efficiently solve on a classical computer; indeed, we currently believe so strongly in the hardness of this problem that an entire cryptographic system (i.e. a method for encoding and decoding information or messages) is based on it! However, it was shown way back in 1994 that a ‘quantum computer’ (i.e. a computer exploiting the laws of quantum mechanics) could efficiently solve the problem of splitting an integer into its prime factors. This is a hugely important result, since it essentially means that if and when it becomes feasible to build quantum computers, the enormously popular RSA cryptosystem will be breakable.
It is probably fair to say, therefore, that building a quantum computer is Kind Of A Big Deal. A wide range of different physical architectures, with various strengths and weaknesses, have been proposed and investigated for building a quantum computer. A string of ions trapped in a Paul trap currently forms one of the most promising architectures, at least in terms of proven experimental results.
Probing an ion with laser light
Of fundamental importance to any use of trapped ions is the controlled interaction of an ion with a focused beam of laser light. Despite its importance, the basic process that occurs when a laser beam strikes an ion (or a neutral atom) is straightforward, and can be understood with the help of the following model.
Firstly, let us assume that the outermost electron in the ion can occupy one of only two possible energy levels. We label these energy levels (or states) A and B. Further, let us assume that the laser light is of exactly the right frequency that (energy of state A + 1 photon of light) = (energy of state B) is a true statement. In this case, the photons in the laser beam have precisely the right energy to promote the electron from state A to state B; we say that the laser is resonant with the A-B transition.
When the resonant laser beam strikes the two-level ion, the electron absorbs energy from the light and is promoted from state A to state B. However, this happens in a very curious way: the electron does not simply jump from A to B and then stay there, but instead begins to oscillate between the states: when the laser is first switched on, the electron is in state A; after (say) 10 microseconds interacting with the laser, it is in B; after 20 microseconds, in A; after 30, back in B, and so on. The frequency of these oscillations is determined by the laser intensity: a stronger laser would cause the electron to oscillate between A and B more rapidly.
Superposition states, and the problem of decoherence
Now a simple but penetrating question presents itself: if the electron is in state A when the laser is first switched on, and state B 10 microseconds later, what kind of state is it in at an intermediate time – say, 5 microseconds? Is it in state A, or state B, or some mixture of the two?
If you picked the third option: well done! It turns out that after 5 microseconds the ion is actually in a state that is best written as “A + B”. If the ion is measured at this instant, it is found in state A with 50% probability, and state B with 50% probability. This “A + B” state is an example of what’s known as a ‘superposition state’: the ion is, in a very real sense, in “both A and B at the same time”.
This superposition state is uniquely quantum-mechanical (classical physics doesn’t allow anything to be in two states “at the same time”!), extremely useful, and also very fragile: as soon as the ion is measured, it is forced to “choose” whether it is “actually” in state A or state B, and its state changes in accordance with the result that we find. For example, if a measurement of the ion finds it in state A, then at the same time the measurement actually forces the ion back into state A. In the language of the field, the very act of measurement ‘collapses’ the superposition “A + B” back to A (or B, if the result of the measurement was state B).
The fact that measuring a trapped ion actually affects the state of the ion has an unwelcome, if interesting, side effect. While trapped ions are generally very well isolated from the surrounding environment, experimental imperfections and noise, such as stray electric and magnetic fields, are always present. It turns out that such experimental imperfections have an effect on superposition states similar to an act of measurement: that is, they act to destroy fragile superposition “A + B”-type states. How to best prepare and protect superpositions, even in the presence of experimental noise, is thus an important and ongoing topic of research.
Conclusion
So this, in a nutshell, is what David Wineland’s research is all about: finding clever ways to trap and manipulate ions with combinations of electric fields and laser light; to prepare fragile superposition states and to protect them from interactions with the environment; and to use these uniquely quantum-mechanical states as a resource to build atomic clocks and perhaps, one day, a trapped ion quantum computer. What a great job to have!
In this post he gives an overview of the field of trapped ions, describes two of its most important applications, and describes what goes on behind the scenes when a trapped ion interacts with a laser beam.
David J. Wineland – probing trapped atoms with light
David Wineland, an experimental physicist at the National Institute for Standards and Technology (NIST) in Boulder, Colorado, is one of the leading researchers in the field of trapped ions: that is, the study of how positively-charged ions (i.e. atoms stripped of one or more electrons) may be trapped, cooled, and manipulated. This field shares many similarities with experiments on neutral atoms (laser cooling, for example, is just as useful for ions as it is for neutral atoms), but also has a number of significant differences. The most important difference that distinguishes ions from atoms is, obviously enough, the fact that ions have a non-zero net electrical charge. This has two very important consequences.
Trapped ions: trapping and interactions
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| A string of trapped ions (red dots) lined up in a Paul trap can be imaged with a tightly-focused laser beam and CCD camera. Image credit: Rainer Blatt experimental group, University of Innsbruck. |
Applying an electric field to an ion produces a force on the ion: positive ions are drawn in the direction of the field. [In contrast, applying an electric field to a neutral atom changes the ‘shape’ of the atom slightly, since the positively-charged nucleus and negatively-charged electron cloud are drawn in opposite directions, but produces no net force.] Consequently, whereas traps for neutral atoms must rely on combinations of laser light and magnetic fields, ions can be trapped just by electric fields. Most of the recent trapped-ion experiments use some variation on the Paul trap (a.k.a. the quadrupole ion trap) which uses a combination of static (DC) and oscillating (AC) electric fields to trap ions along a 1-dimensional line.
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| Images of ion strings containing (L to R) 1, 2, 3, 6, and 'some' ions. These images were created by using laser light to illuminate the ions in the string. Image credit: phys.org |
The second important point is that ions interact with one another far more strongly than neutral atoms do: two positive ions repel one another strongly through their mutual Coulomb interaction. [In contrast, neutral atoms typically interact very weakly, and behave essentially like hard spheres: they are ignorant of the presence of one another unless in direct contact.] Consequently, ions held in a Paul trap are subject to two competing tendencies. Firstly, the ions are drawn towards the center of the trap in order to minimize the trapping potential energy; secondly, they strongly repel one another in an attempt to minimize the ion-ion interaction energy. By way of compromise, the ions line up like a string of beads, with inter-ionic distances of the order of a few tens of microns. This is, experimentally speaking, a very convenient state of affairs, since it means that each ion can be individually addressed by a tightly-focused laser beam.
Applications of trapped ions
Strings of laser-cooled ions held in a Paul trap can be put to a variety of uses. One important application lies in the realm of high-precision spectroscopy and frequency standards. Securely trapped, well isolated from the environment, and cooled to a standstill, a single laser-cooled ion in a Paul trap is an ideal subject on which to make precision energy-level measurements (or, equivalently, measurements of the frequency of the electromagnetic radiation that the ion absorbs and emits).
Since frequency is just the inverse of time, a well-defined frequency can be used as a reference point for defining exactly what a ‘second’ is. Single trapped ions thus form an excellent basis for atomic clocks. Such clocks show significantly improved accuracy over those based on the radiation emitted by neutral cesium atoms (the kind which, since 1967, has formed the basis for the SI definition of a second).
 |
Storing information in the electronic state of a single ion or atom opens the door to the development of information-processing schemes that take advantage of quantum mechanics. |
A second important application of trapped ions is their use in the field of quantum information processing (a.k.a. quantum computing). This field is founded on the realisation that the laws of quantum mechanics appear to allow for a more powerful model of computation than the (classical) Turing paradigm that underpins computing as we know it. Although this result hasn’t yet been mathematically proven, at this point in time it seems extremely probable that computers that are designed to take advantage of the intricacies of quantum mechanics can efficiently solve problems that are completely intractable for a classical computer.
The best-known example of such a problem is the division of a large integer into its prime factors (e.g. 15 = 3*5; or 70 = 2*5*7) This task is generally believed to be impossible to efficiently solve on a classical computer; indeed, we currently believe so strongly in the hardness of this problem that an entire cryptographic system (i.e. a method for encoding and decoding information or messages) is based on it! However, it was shown way back in 1994 that a ‘quantum computer’ (i.e. a computer exploiting the laws of quantum mechanics) could efficiently solve the problem of splitting an integer into its prime factors. This is a hugely important result, since it essentially means that if and when it becomes feasible to build quantum computers, the enormously popular RSA cryptosystem will be breakable.
 |
| This image came up when I Googled 'quantum computer'. It's kind of cool. Unfortunately, any quantum computer that we do end up building is unlikely to look like this. Image credit: extremetech.com |
It is probably fair to say, therefore, that building a quantum computer is Kind Of A Big Deal. A wide range of different physical architectures, with various strengths and weaknesses, have been proposed and investigated for building a quantum computer. A string of ions trapped in a Paul trap currently forms one of the most promising architectures, at least in terms of proven experimental results.
Probing an ion with laser light
Of fundamental importance to any use of trapped ions is the controlled interaction of an ion with a focused beam of laser light. Despite its importance, the basic process that occurs when a laser beam strikes an ion (or a neutral atom) is straightforward, and can be understood with the help of the following model.
Firstly, let us assume that the outermost electron in the ion can occupy one of only two possible energy levels. We label these energy levels (or states) A and B. Further, let us assume that the laser light is of exactly the right frequency that (energy of state A + 1 photon of light) = (energy of state B) is a true statement. In this case, the photons in the laser beam have precisely the right energy to promote the electron from state A to state B; we say that the laser is resonant with the A-B transition.
When the resonant laser beam strikes the two-level ion, the electron absorbs energy from the light and is promoted from state A to state B. However, this happens in a very curious way: the electron does not simply jump from A to B and then stay there, but instead begins to oscillate between the states: when the laser is first switched on, the electron is in state A; after (say) 10 microseconds interacting with the laser, it is in B; after 20 microseconds, in A; after 30, back in B, and so on. The frequency of these oscillations is determined by the laser intensity: a stronger laser would cause the electron to oscillate between A and B more rapidly.
Superposition states, and the problem of decoherence
Now a simple but penetrating question presents itself: if the electron is in state A when the laser is first switched on, and state B 10 microseconds later, what kind of state is it in at an intermediate time – say, 5 microseconds? Is it in state A, or state B, or some mixture of the two?
If you picked the third option: well done! It turns out that after 5 microseconds the ion is actually in a state that is best written as “A + B”. If the ion is measured at this instant, it is found in state A with 50% probability, and state B with 50% probability. This “A + B” state is an example of what’s known as a ‘superposition state’: the ion is, in a very real sense, in “both A and B at the same time”.
This superposition state is uniquely quantum-mechanical (classical physics doesn’t allow anything to be in two states “at the same time”!), extremely useful, and also very fragile: as soon as the ion is measured, it is forced to “choose” whether it is “actually” in state A or state B, and its state changes in accordance with the result that we find. For example, if a measurement of the ion finds it in state A, then at the same time the measurement actually forces the ion back into state A. In the language of the field, the very act of measurement ‘collapses’ the superposition “A + B” back to A (or B, if the result of the measurement was state B).
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| I couldn't find a good picture of a quantum-mechanical superposition collapsing due to the act of measurement, so to congratulate you on getting this far, here's a picture of a sloth. He also seems to have collapsed to his lowest-energy state upon being measured. Perhaps sloths are quantum systems? Image credit: here. |
The fact that measuring a trapped ion actually affects the state of the ion has an unwelcome, if interesting, side effect. While trapped ions are generally very well isolated from the surrounding environment, experimental imperfections and noise, such as stray electric and magnetic fields, are always present. It turns out that such experimental imperfections have an effect on superposition states similar to an act of measurement: that is, they act to destroy fragile superposition “A + B”-type states. How to best prepare and protect superpositions, even in the presence of experimental noise, is thus an important and ongoing topic of research.
Conclusion
So this, in a nutshell, is what David Wineland’s research is all about: finding clever ways to trap and manipulate ions with combinations of electric fields and laser light; to prepare fragile superposition states and to protect them from interactions with the environment; and to use these uniquely quantum-mechanical states as a resource to build atomic clocks and perhaps, one day, a trapped ion quantum computer. What a great job to have!
Unrelated to this post itself, but wanted to say that I very much like the new look Trenches. The font size and colour are much easier to read, and the links look better. Well done!
ReplyDeleteShhh, I was hoping my blog collaborators wouldn't notice!
DeleteThe old form didn't irk me until you pointed it out in an email almost a year ago and it has slowly been wearing me down ever since until I broke sometime last weekend. I'm glad you like the links because that was the one remaining thing I was a little unsure of.