Optomechanics IV - André Xuerebandre.xuereb.info/files/OM_4.pdf · Testing quantum mechanics…...

Optomechanics IV

André Xuereb, University of Malta ([email protected])

Winter School on Physics of Small Quantum Systems, 16th January 2015

Credits

This series of lectures draws heavily from a lecture by Klemens Hammerer, called “Quantum Optomechanics” and delivered at the QLNO Summer School in August 2010.

Overview of this lecture

▪ Optomechanics paradigms– Various common geometries

– Dissipative optomechanics

– Many-mirror optomechanics

▪ Quantum thermodynamics with optomechanics

▪ Testing quantum mechanics… with optomechanics

The various geometries: End-mirror

▪ The first geometry investigated was the “end-mirror” geometry

[M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, arXiv:1303.0733 (2013)]


▪ Really massive mirrors (g scale) are used in gravitational-wave detectors

▪ This is where optomechanics traces its origin, in the 1970s!


▪ The first cavity optomechanics mirrors were performed using this sort of mirror

▪ Whilst simple to manufacture, barriers quickly arose


▪ Newer techniques of manufacturing suspend mirrors in complex geometries

▪ Such systems shield the mirror from thermal vibrations

The various geometries: In-cavity

▪ A very popular alternative is placing objects inside a cavity

▪ Pioneered by the Harris group in Yale using cheap ($15) membranes, this technique has opened many doors (including 𝑥2 and 𝑥4 coupling)


The various geometries: On-chip

▪ We have seen that 𝑔 ∝ 1/ 𝑚, so smaller systems are favourable

▪ It was this kind of system that first achieved ground-state cooling and entanglement between light and motion



▪ A fruitful alternative has been to go from optics to microwaves

▪ Microwave circuit QED is very advanced, and microwave optomechanics leads the way in some aspects

▪ It also enables translation of signals from microwaves to light, or vice versa


▪ Also highly exciting is using optomechanical crystals

▪ These are photonic crystals that trap light and sound in the same place

▪ Pioneered by the Painter group in Caltech, these have proven very versatile

The various geometries: Toroidal

▪ Toroidal optical cavities can have very high qualities

▪ They also vibrate, creating a naturally self-contained optomechanical device



▪ A flat pancake of silicon, under the right conditions, possesses “whispering-gallery modes”

▪ These modes are very sensitive to changes in the radius


▪ Once again, one can optimise the design

▪ Adding spokes and creating spaces in the structure improves its mechanical quality


▪ Many variations are possible, including ones with two wheels

▪ Vertical vibrations change the properties of the light field confined between the wheels

The various geometries: Hybrid

▪ Atoms also move and interact with the light field!

▪ Hybrid optomechanical setups allow interfaces between light and, e.g., spin systems



▪ One kind of geometry has atoms localised on a standing wave supported by a vibrating mirror

▪ The two systems can influence each others’ motion

▪ Cold atoms can be used to cool the mirror motion down


▪ In another kind of system, one does away with “mirrors” entirely

▪ Groups of atoms act as a tiny mirror inside a cavity

▪ Having an extremely small mass makes these systems ideal for strong-coupling experiments

Dissipative optomechanics

▪ In 2009, Elste, Girvin, and Clerk proposed a completely different paradigm

▪ So far, we have discussed the mechanism where𝜔c → 𝜔c 𝑥

▪ Despite being tremendously interesting, there are some limitations for this mechanism

▪ One is that in order to cool down to very low occupation numbers, 𝜅 ≪ 𝜔m is required, which is often a tough requirement


▪ What was proposed was fundamentally different, a system where𝜅 → 𝜅(𝑥)

▪ Under certain conditions, such a dissipative system would outperform a traditional (dispersive) one

▪ In 2011 Klemens Hammerer, Roman Schnabel, and I showed how this could be engineered in an interferometric geometry

▪ Earlier this year, the first experimental evidence of this mechanism was published


[A. Xuereb, R. Schnabel, and K. Hammerer, Phys. Rev. Lett. 107, 213604 (2011)]


[A. Sawadsky, et al., arXiv:1409.3398 (2014)]

Optomechanics with many mirrors

▪ When discussing the coupling strength 𝑔, I ignored the reflectivity of the mirror

▪ Solving Maxwell’s equations yields

𝑔 =ℏ

2𝑚𝜔m

𝜔c

𝐿𝑅

▪ Thus, the lower the power reflectivity 𝑅, the smaller 𝑔 is

▪ This is obvious: A transparent “mirror” should have no effect


▪ In any case, having a mirror with fixed mass and frequency, and a cavity with fixed length, there are few variables

▪ In fact, one can only increase 𝑔 by trying to get 𝑅 → 1

▪ This means making better and better mirrors


[S. Gröblacher, et al., Nature Phys. 5, 485 (2009)]


▪ We discovered an interesting alternative

▪ Suppose the different layers in the mirror were free to move

▪ What happens as we change the spacing between them?


[A. Xuereb, C. Genes, A. Dantan, Phys. Rev. Lett. 109, 223601 (2012)]


▪ By making the compound mirror worse (𝑅 = 0!) we found a way to increase 𝑔 dramatically

▪ One way of understanding what is going in is to realise that the array “concentrates” the field between the mirrors

▪ This system has a few interesting advantages:– It allows for very strong coupling

– Each mirror is coupled to every other

– Different forms of mirror–mirror couplings can be chosen by changing the light frequency

Quantum thermodynamics

▪ Many of us associate “thermodynamics” with steam engines

▪ A recent effort has seen the concepts of 19th century thermodynamics being ported to the quantum regime

▪ These concepts were covered in the lectures by Takahiro Sagawa so I will not dwell on them

Very classical thermodynamics

Very classical thermodynamics

[“How Steam Engines Work,” howstuffworks.com]


▪ There are several apparent parallels between steam engines and optomechanical devices

▪ Because of this it is natural to think of whether one can produce “optomechanical engines”

▪ Many ideas have been put forward, but I’ll simply mention one that I was involved in


▪ We imagined a system where 𝑔 can be controlled at will

▪ So, suppose 𝑔 = 0 for 𝑡 < 0

▪ At 𝑡 = 0, we switch on the interaction between light and motion

▪ We asked: What happens?


▪ We looked specifically at the statistics of the work done on the motion of the mirror by the interaction

▪ Interesting (or not?), 𝑊 = 0: Half the time the field does work on the mirror, the other half the mirror on the field


[M. Brunelli, et al., arXiv:1412.4803 (2014)]


[P. Rabl, Phys. Rev. Lett. 107, 063601 (2011)]

Beyond “quantum”?

▪ Optomechanics is a unique tool in physics

▪ It combines things we have extreme control over, i.e., measuring and manipulating electromagnetic fields, with objects that can be “macroscopic” according to many definitions

▪ I want to look at three possibilities afforded by optomechanics– Non-classical interferometry

– Superpositions of massive objects

– Beyond quantum mechanics

Non-classical interferometry

▪ Optomechanics started as a field in the 1970s when people were thinking of building interferometric gravitational wave detectors

▪ These detectors are “simple” Michelson interferometers, with perpendicular arms

▪ The theory is that a passing gravitational wave changes the relative lengths of the two arms


▪ The detectors need to be large because the changes in distance are minute

▪ Gravitational wave detectors must balance:– The signal, whose power increases with power input into the interferometer

– The noise, which also increases with power

▪ One source of noise is radiation pressure noise, which I mentioned in Lecture II

▪ By using squeezed light, the precision of a gravitational wave detector may be increased significantly


[The LIGO Scientific Collaboration, Nature Phys. 7, 962 (2011)]


▪ Optomechanics enters the equation in two ways

▪ First, cooling the motion reduces the noise in the interferometer

▪ Second, features of non-classical light may be transferred to the motion of the mirror, which may improve the readout further

Superpositions of massive objects

▪ The duality between waves and particles is one of the oldest curiosities in quantum mechanics

▪ One question is: Up to which mass and length scale is it possible to observe superpositions of objects?

▪ Two programmes being followed:– The “bottom-up” approach of building larger and larger molecules and

observing non-classical interference patterns

– The “top-down” approach of optomechanics, which makes smaller and smaller structures until non-classical features are observed


▪ Whereas entanglement of light with motion has been observed, a macroscopic superposition of a “large” object has proven elusive thus far

▪ The reasons are fairly mundane: Large objects have lots of contact with the outside world, which tends to destroy superpositions

▪ But is it just an engineering issue, or does the universe itself prohibit such massive superpositions?

Beyond quantum mechanics

▪ The (non)observation of massive superpositions is not the only way to probe whether nature is quantum mechanical at every scale

▪ It has been proposed to use optomechanics to measure a very fundamental object:

𝑥, 𝑝


▪ The idea is to use pulses to shift the mechanical oscillator

▪ By carefully timing the pulses, it may be possible to reveal a difference from

𝑥, 𝑝 = 𝑖ℏ

▪ A “table-top” experiment such as this could allow us to invalidate theories that would otherwise require large-scale experiments


[I. Pikovski, et al., Nature Phys. 8, 393 (2012)]

End of Lecture IV

Any questions?

Thanks to…

I am indebted to many people with whom I’ve worked over the past years:

▪ Southampton: Tim Freegarde, Peter Horak, Hendrik Ulbricht

▪ Budapest: Péter Domokos, János Asbóth

▪ Hannover: Klemens Hammerer, Roman Schnabel

▪ Belfast: Mauro Paternostro, Matteo Brunelli, Lorenzo Fusco

▪ Arhus: Aurélien Dantan

▪ Innsbruck: Claudiu Genes

▪ Strasbourg: Guido Pupillo

End of Course

I hope that you have understood at least most of what I said.

Optomechanics is a thriving field; I have tried to give you an overview.

Finally, I hope you enjoyed it!

Don’t forget my email: [email protected]

Optomechanics IV - André Xuerebandre.xuereb.info/files/OM_4.pdf · Testing quantum mechanics…...

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