A spring in my step: quantum coherence in bosons

Recently we had some good news – our paper has been published in Physical Review A (open access version here). So I’m going to digress from the usual format of this blog and explain our research for the non-technical reader. Enjoy!

 

Quantum physics, the description of our Universe on very small scales, has been around for about a century now, and it has some astonishing predictions. Particles can ‘tunnel’ through walls and an electron can even travel through two slits simultaneously and then interact with itself. What’s more astonishing is that the predictions made by quantum mechanics have been verified in thousands of experiments, confirming that our Universe is, well, odd.

Quantum revolutions

We’ve been using the quantum properties of matter to our advantage for decades now. Quantum mechanics allows us to describe the structure of the atom, the periodic table, semiconductors and much more. The advances in quantum theory that were made at the beginning of the twentieth century have been dubbed the “first quantum revolution”. The subsequent progress in semiconductor physics has led to the technological revolution we’re seeing today, in which computers more powerful than the one that first sent humans to the moon now sit inside your toaster.

The advances brought about by the first quantum revolution came from understanding how large groups of electrons behaved inside different materials. Then materials with the desired properties could be made, for example by doping semiconductors in order to build complex structures like LEDs.

Now, we’re starting to understand how to exploit other quantum phenomena, such as superposition, in what one might call the second quantum revolution. Superposition lies at the heart of many proposed quantum technologies, such as quantum computing, quantum sensors, quantum cryptography and more. Superposition is also a profoundly quantum property, with no classical (“everyday”) equivalent, so what follows is an analogue.

Superposition and coherence

Suppose you have a coin, and you flip it. There’s 50% chance that it will show heads; 50% tails. We don’t know which it will be on any given flip, but we know it will be one or the other. That’s a “classical” coin. Now suppose you take your coin and set it spinning on the table. That coin isn’t showing either heads or tails; in some way it is partly in both states at the same time. In our analogy, our “quantum” coin is now in a superposition of heads and tails. Unlike our classical coin, it has coherence.

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A spinning coin is like a quantum particle in superposition: neither entirely heads nor tails, but somehow both at once. Picture credit: 68lbs_on_flickr

 

Coins (even quantum ones) don’t spin forever, and sooner or later our coin will stop spinning, due to friction, to air resistance, or due someone knocking the table. In other words, the rest of the world interacts with our coin and disrupts it. How quickly this happens depends on the exact conditions of the surrounding environment, but it will always happen sooner or later. When our coin stops, it falls over onto one side, and becomes like a classical coin again. We say that it has decohered.

Decoherence is a big problem when building a quantum computer – quantum computers rely on keeping many particles in a superposition and using them to do calculations. But these particles quickly decohere, losing their quantum information. Understanding and working out how to control decoherence is a big priority for quantum physics research today.

A pair of tiny quantum springs

We already have maths that describes what happens when one single quantum particle interacts with its surroundings and loses coherence; however things get trickier when there are two (or more!) particles in the mix. The type of particles we were looking at in our paper are called bosons, and they can be thought of as being like very tiny springs. Imagine that our two tiny springs are joined together by a rod, so that as one bounces back and forth, it affects the motion of the other, and vice versa.

Boson Spring Diagram
Coupled bosons can be thought of as two tiny springs joined together. When they lose quantum information to their surroundings, do they do so individualy (1) or as a joint mega-spring (2)? Picture credit: Philip Cammack

Our question was: how does joining the two springs together affect their decoherence? There were two possible approaches:

  1. The springs would behave as though they weren’t joined, and each one would decohere at its own rate, regardless of what was happening to the other one.
  2. The springs would act like a single mega-spring, and this mega-spring would decohere all at the same rate.

Approach #1 works well when the two springs are only loosely joined (e.g. by a slack piece of string). Approach #2 is great when our two springs are joined tightly by a rigid rod, so that one cannot move without greatly affecting the other one. But what do we do when the joining falls somewhere between these two extreme cases? We found a method of dealing with intermediate cases in a consistent way which takes account of both the joining between the springs and the differing rates at which the two springs decohere.

What next?

The work in our paper uses particles called bosons, but there’s another type of particle in town: the fermion. In fact, everything is made up of bosons and fermions. Examples of bosons include photons (particles of light) and particles such as gluons and the Higgs , most familiar to particle physicists. Fermions make up the matter around us, such as electrons and quarks (these form protons and neutrons which in turn form atomic nuclei).

Now that we understand how a pair of bosons decohere, there are two avenues of research open to us. Firstly, we can use our method and extend it to look at a larger collection of bosons, and understand their decoherence. The second is to use similar techniques to derive a method for dealing with two fermions which are joined together. It’s this second question that has been preoccupying me, and we’re close to getting some exciting results on that one, so sit tight and hopefully there’ll be more news on that question soon.

 

Women in physics: personal perspectives

Following the IOP’s “Taking Control of your Career as a Female Physicist” event, I spoke with Dame Professor Athene Donald and Professor Val Gibson about their careers within academia.

 

Since I entered the third year of my PhD, my future career has been increasingly on my mind. I’ve been to a few careers events with stands full of free USB pens and glossy brochures, but always came away disappointed, unable to see myself in the roles they had advertised. The IOP’s careers event was different; there, people shared my aspirations and were sympathetic to my concerns. The opening talk by Prof Athene Donald was inspirational, and there was a variety of guest speakers who had used their physics training to build successful careers. I came away from the day with a new buzz, excited about my career possibilities.

 

What has been the most enjoyable part of your career?

AD: My postdoc in the U.S.: postdocs offer a combination of independence and freedom that you don’t often get later on in your career.

VG: Being a postdoc is one of the most exciting times of your life. When I had my CERN Fellowship I was free to do what I liked, and I ended up running my own experiment and working with some fantastic people.

 

Do you think quality or quantity of papers is most important for a young researcher just starting out?

VG: I think you need absolute enthusiasm for your subject and the quality of your research is key. It’s not about the quantity of publications.

AD: And it’s not impact factor. I’m a signatory for DORA. My postdocs push me about where to publish and I feel that’s the wrong way to go. In my field, people wait until results are absolutely complete rather than putting out results quickly to stimulate further debate.

VG: In my field, the papers we put out now have been internally reviewed by the large collaborations to death, and sometimes you can wait six months to a year for results to come out. It’s highly demoralising for the young researchers – you have to go through so many reviews and editorial procedures that by the time the paper comes out you’re exhausted.

 

As you progress in academia, you start to pick up other commitments such as teaching, supervising and sitting on committees. Are these unwelcome distractions from research, or a breath of fresh air?

AD: It’s variable. When I was relatively junior, I was put on a grant committee which was a real eye opener. However, you can get stuck on committees that aren’t very interesting but can be time consuming. One of the skills is learning when to say no. When you’re junior, any committee can be eye opening.

VG: Research tends to suffer when you take on other commitments, but as you become more senior in academia, you most likely have a research group working with you. At some point you don’t have time to do the day to day technical aspects of the research, but you can look at the overall picture, and guide your research group towards what you think is worthwhile. I think that’s a very big step for an academic, to stand back and let your research group run, working with them on new ideas.

 

What’s the aim of gender equality, and do you think this is an achievable goal?

VG: I believe we can ultimately achieve a so-called “horizontal leaky pipeline,” such that the percentage of women in physics remains constant throughout career levels. The trick is to increase the percentage of women who come into physics in the first place, and that requires a major change somewhere in earlier education and within the home environment. In school, boys tend to do science alongside subjects such as computing and engineering, whereas girls who study physics often haven’t acquired those other useful skills.

AD: Undoubtedly the problem starts way before university. But I’m not convinced that 50:50 in every subject is the right place to be; we don’t actually know where the balance lies. Within academia, there are still men and women who think that a women’s primary role is to bring up a family, and it’s those attitudes that will continue to hold women back The view that men are the breadwinners is endemic in our society – there’s the belief that men ‘need to get on’ and that the system should make that possible.

 

Did you relocate often as a postdoc?

AD: I moved around – I had a postdoc in the States, then returned to Cambridge. But at that stage I wasn’t really thinking about a career, so I wasn’t that bothered about what happened next. I didn’t intend to be an academic, so the pressure wasn’t on me. Nowadays everyone has to be calculating and publish in the right journals, and the pressure can detract from that freedom.

VG: When I was in my early career, I was just enjoying the moment, and I wasn’t thinking about my future career. The postdocs of today seem to more aware about career opportunities; they know that the majority of them won’t stay in academia; they’re looking around for what they would like to do and they’re picking up the skills they need for the future. It’s not just the academic side, it’s also the personal aspects – they’re concerned about getting on the housing ladder and potentially having families. At that stage those concerns never crossed my mind.

 

How well do you think academia prepares graduates for careers outside of academia?

VG: Not well enough, although they do obtain quite a few skills that they probably don’t recognise as being very useful, such as communication, writing and computing skills. We cannot train them in all aspects of potential future careers, so it is important that they also engage with suitable training schemes.

AD: You could argue that it’s the role of the careers services within universities rather than that of the PIs to talk about what’s available outside. I’ve been in academia my whole life – what do I know about the outside world? Careers advisors are much better placed to advise graduates about a life outside academia, although we should stress transferable and soft skills where we can so that the graduates appreciate what they’re learning as they do their research.

 

Which skills tend to be neglected during a PhD in academia?

AD: We don’t do much on project management or interpersonal skills. We do lots of analytical skills, critical thinking, reading and writing.

VG: I would add leadership skills, because working in large collaborations it helps to be able to interact with large numbers of people.

 

Do you have any advice for a young researcher on a committee who wishes to put an idea forward at a meeting with senior academics?

VG: Don’t be intimidated. If you have an idea that is good, you should share it at an appropriate time and you’ll be heard.

AD: It depends on the type of committee, but sometimes it’s useful to find allies for a certain idea before the meeting. Work out what the counter-arguments will be so that you’re prepared. Be articulate, concise and audible.

VG: A good chair would make sure that everyone in the room has a voice, so if you have something you’d like to say, it’s a good idea to talk to the chair beforehand.

 

Do you have any tips for PhD students who suffer from imposter syndrome?

AD: It’s valuable to recognise that everyone suffers from this, even professors!

VG: You may learn more physics and research as you go along, but you recognise there’s a lot you don’t know and you feel your inadequacies through that. It’s always there.

AD: Knowing you can cope with it is what changes, and that it’s not the end of the world if you say you don’t know something.

VG: It helps to give yourself a pat on the back every so often, and realise that you can do what you’re planning to.

 

If a time machine took you to meet yourself at the end of your first degree, what would you say?

VG: I would say that maybe I should have listened more in lectures!

AD: I would tell myself not to compare myself with other people, and to work out who you are.

VG: Take advice, but don’t be influenced by other people or told what to do. You should make the decisions for your future. Do the things you enjoy, and you’ll do well.

 

 

Dame Professor Athene Donald is Professor of Experimental Physics at the University of Cambridge and Master of Churchill College. From 2010-14 she was the University’s Gender Equality Champion.

Professor Val Gibson is Professor of High Energy Physics at the University of Cambridge, a Senior Gender Equality Champion, and Fellow and Director of Studies at Trinity College. She is also Chair of the Institute of Physics’ Juno Panel.

 

The original articles can be found here and here.

Update: going travelling

Today is the last day of my research visit to the University of Queensland (see the benefits of research trips and learning something new) and I’ve got a lot of food for thought, and the start of what promises to be a very interesting and complex project. Now I’m going travelling, so this blog will fall quiet until the end of February. When I return I’ll be starting a three-month internship with Education Scotland – watch this space for more info about that!

Learning something new

Whilst on this research trip I’ve been trying to get my head around a new topic, quantum stochastic processes (stochastic processes have a certain amount of “noise” and are used for modelling all sorts of things, including stock markets). Getting to grips with any new area requires a lot of dedication, some really good resources, and (ideally) someone patient enough to sit with you and answer all your questions. When you’re struggling with a new topic, it’s normal to feel like you don’t understand any of it. It’s normal to think that you will never make any sense of the material in front of you; that this is beyond you and that you’re not clever enough. It’s normal to want to give up, to throw the textbook across the room and get a job at Tesco’s.

Frustrated: fifth attempt at the same calculation

 

I’ve thought these thoughts (and more) every time I try and teach myself a new topic. It’s a painful process. But until we sit down with the material that we don’t understand, we don’t know the limits of our knowledge. The first step to learning something new is discovering what we don’t know and exploring the limits of our understanding. This can be frustrating and demoralising. “I thought I understood X”, you say to yourself; “if I don’t even understand that, then obviously I don’t understand anything else either!” Cue massive confidence crisis and general feelings of unworthiness and misery.

Before you fill in the Tesco’s job application form though, consider this: by realising that you don’t understand something, you have taken a step towards learning it. That’s probably the most painful step in learning, and it’s one we’re not given much guidance on dealing with. Whilst at school, high flyers don’t often experience the feeling of not being able to understand something, and the first year of university comes as a shock to many who were used to getting 100% on their school homework assignments. It can be very difficult to make that adjustment; to go from thinking that your understanding of the universe is basically complete to realising that your knowledge is shaky, incomplete and often wrong.

During a PhD, the inconvenient truth of your incomplete knowledge is brought home, day in, day out, often brutally. It’s no wonder that PhD students often doubt themselves and their capabilities; they’re coming up against the limits of their understanding on a daily basis. “I’m so stupid”, they say, “I can’t even put the optical master equation into Lindblad form!” What they often forget is that not only does this make absolutely no sense to the majority of the population, but also that probably made no sense to them until relatively recently. To know you can’t put something in Lindblad form, you first have to know what Lindblad form is.

It also doesn’t help your confidence that everyone else around you at work is throwing around Lindblad equations like they were born doing it. But remember: this is just an act, a clever disguise. Academics make a career out of being smart, so it pays for them to look smart. They weren’t actually born knowing all of physics, they had to learn this stuff too. This means they’re in a great place to help you learn it. So ask them questions, again and again, because in my experience books can only take you so far. You’ll need someone to thrash ideas out with, to explain those sticky points and correct you when you go wrong. With patience, perseverance and (probably) some help, you’ll get there. But before you move onto the next thing you don’t understand, take a moment to congratulate yourself. You learnt something new.

The benefits of research trips

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Life down under: a koala takes it easy

I’m now a fortnight into my Australian trip, and things are panning out well. The heat is tolerable, the sunshine welcome, the people friendly. I’m on first name terms with the waiters in the coffee shop, the college chefs and the porters. The Aussie sunshine has turned me (much to my surprise) into an early riser; 6am is so much more pleasant here where the birds sing, the warm air is fresh and the sun is already poking its head above the horizon.

Lest anyone think this is all just a glorified holiday, I’ve been learning a lot here too. My collaborator here is focused and has an excellent understanding of the problem I’m working on and the tools I’m using to tackle it. I’ve gained a lot from our frequent chats over coffee in the shade of the eucalyptus trees in the corner of the quad. I’ve learnt new techniques and understood new pieces of physics. But more than that; I’ve participated in all sorts of research discussions, heard new ideas, seen new perspectives. And I think this is the most valuable thing about travelling; your viewpoint literally alters. You get the opportunity to look at the world anew and get a fresh perspective on things.

Prior to coming out here, I had been working on the same project for months – it had turned into a monstrous hydra, growing three new heads for every one that was cut off. I needed a break. I needed a fresh start. That’s what Australia has given me – a fresh project to sink my teeth into and fresh ideas to get my head around.

There are other benefits to working away from home, particularly somewhere far away: due to the time difference, emails don’t come into my inbox during working hours. I don’t have all the usual obligations of work – no seminars to attend, no colloquia, no tutorials to give. It’s amazing how much more one can do in a day that isn’t punctuated by constant distractions and commitments. The sunshine has cured me of my usual winter lethargy, giving me extra energy and making me more productive. Besides which, I’m enjoying it all – the weather, the wildlife, the flowers, the sights and smells. Now, how do I turn the temperature down by a couple of degrees?

To seize an opportunity, first you need to create it

On Saturday I’m travelling to Australia for a month-long research trip. I’m excited and nervous and a little bit scared, and it’ll be hard to be away from my other half for so long. But this is a fantastic opportunity for me, and I’m definitely looking forward to a breath of fresh air (and sun!) and a chance to get to grips with a different research project and meet new collaborators.

My supervisor first mentioned the idea of a trip to Australia around a year ago, and my response was enthusiastic. However, other PhD students warned me that they had had similar offers, but they had come to nothing. I realised that if I really wanted to make this trip happen, I would need to be proactive. In order to seize the opportunity, I first had to create it.

A few days before the deadline, I applied for a scholarship fund for PhD students from the UK to travel to an Australian institution for a research visit. The application included a research proposal which I constructed with help from my supervisor and our Australian collaborator. We had some detailed discussions about the project that I would be given, and agreed rough dates for the visit. My scholarship application was successful, and the trip began to feel real – flights were booked, accommodation arranged, visa applied for.

This wouldn’t have happened if I hadn’t been proactive – followed up on my supervisor’s suggestion and pestered him about when the trip would be possible, applied for the scholarship even though it was close to the deadline, contacted our collaborator and discussed the research proposal. Sometimes you have to ask to get something. Sometimes you have to ask more than once. On some occasions you might not get it, but on others you will. You’ve nothing to lose and potentially there’s everything to be gained from asking.