optomechanics iv - andré xuerebandre.xuereb.info/files/om_4.pdf · testing quantum mechanics…...
TRANSCRIPT
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Optomechanics IV
André Xuereb, University of Malta ([email protected])
Winter School on Physics of Small Quantum Systems, 16th January 2015
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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.
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Overview of this lecture
▪ Optomechanics paradigms– Various common geometries
– Dissipative optomechanics
– Many-mirror optomechanics
▪ Quantum thermodynamics with optomechanics
▪ Testing quantum mechanics… with optomechanics
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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)]
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The various geometries: End-mirror
▪ Really massive mirrors (g scale) are used in gravitational-wave detectors
▪ This is where optomechanics traces its origin, in the 1970s!
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The various geometries: End-mirror
▪ The first cavity optomechanics mirrors were performed using this sort of mirror
▪ Whilst simple to manufacture, barriers quickly arose
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The various geometries: End-mirror
▪ Newer techniques of manufacturing suspend mirrors in complex geometries
▪ Such systems shield the mirror from thermal vibrations
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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)
[M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, arXiv:1303.0733 (2013)]
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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
[M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, arXiv:1303.0733 (2013)]
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The various geometries: On-chip
▪ 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
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The various geometries: On-chip
▪ 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
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The various geometries: Toroidal
▪ Toroidal optical cavities can have very high qualities
▪ They also vibrate, creating a naturally self-contained optomechanical device
[M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, arXiv:1303.0733 (2013)]
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The various geometries: Toroidal
▪ A flat pancake of silicon, under the right conditions, possesses “whispering-gallery modes”
▪ These modes are very sensitive to changes in the radius
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The various geometries: Toroidal
▪ Once again, one can optimise the design
▪ Adding spokes and creating spaces in the structure improves its mechanical quality
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The various geometries: Toroidal
▪ Many variations are possible, including ones with two wheels
▪ Vertical vibrations change the properties of the light field confined between the wheels
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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
[M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, arXiv:1303.0733 (2013)]
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The various geometries: Hybrid
▪ 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
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The various geometries: Hybrid
▪ 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
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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
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Dissipative optomechanics
▪ 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
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Dissipative optomechanics
[A. Xuereb, R. Schnabel, and K. Hammerer, Phys. Rev. Lett. 107, 213604 (2011)]
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Dissipative optomechanics
[A. Sawadsky, et al., arXiv:1409.3398 (2014)]
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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
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Optomechanics with many mirrors
▪ 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
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Optomechanics with many mirrors
[S. Gröblacher, et al., Nature Phys. 5, 485 (2009)]
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Optomechanics with many mirrors
▪ 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?
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Optomechanics with many mirrors
[A. Xuereb, C. Genes, A. Dantan, Phys. Rev. Lett. 109, 223601 (2012)]
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Optomechanics with many mirrors
▪ 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
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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
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Very classical thermodynamics
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Very classical thermodynamics
[“How Steam Engines Work,” howstuffworks.com]
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Quantum thermodynamics
▪ 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
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Quantum thermodynamics
▪ 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?
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Quantum thermodynamics
▪ 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
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Quantum thermodynamics
[M. Brunelli, et al., arXiv:1412.4803 (2014)]
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Quantum thermodynamics
[P. Rabl, Phys. Rev. Lett. 107, 063601 (2011)]
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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
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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
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Non-classical interferometry
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Non-classical interferometry
▪ 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
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Non-classical interferometry
[The LIGO Scientific Collaboration, Nature Phys. 7, 962 (2011)]
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Non-classical interferometry
▪ 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
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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
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Superpositions of massive objects
▪ 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?
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Superpositions of massive objects
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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
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Beyond quantum mechanics
▪ 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
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Beyond quantum mechanics
[I. Pikovski, et al., Nature Phys. 8, 393 (2012)]
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End of Lecture IV
Any questions?
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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
![Page 51: Optomechanics IV - André Xuerebandre.xuereb.info/files/OM_4.pdf · Testing quantum mechanics… with optomechanics. The various geometries: End-mirror The first geometry investigated](https://reader035.vdocuments.site/reader035/viewer/2022070113/605d6e0b14b53b23d97936be/html5/thumbnails/51.jpg)
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]