New paper: cooling limits and measurement of optomechanical oscillator

New paper dance now.

arXiv:0906.1379

Title: Phase noise and laser cooling limits of opto-mechanical oscillators
Author: Zhang-qi Yin

Abstract: The noise from laser phase fluctuation sets a major technical obstacle to cool the nano-mechanical oscillators to the quantum region. We propose a cooling configuration based on the opto-mechanical coupling with two cavity modes to significantly reduce this phase noise. After optimization of the cavity parameters, we show through simple arguments that the intrinsic cooling limit of the opto-mechanical oscillator is set by $T_{\text{env}}/Q$, where $T_{\text{env}}$ is the environment temperature and $Q$ is the mechanical quality factor. We also discuss detection of the phonon number when the mechanical oscillator is cooled near the quantum region and specify the required conditions for this detection.

Update in 17th June: Today I found a similar paper published in PRL: Three-Mode Optoacoustic Parametric Amplifier: A Tool for Macroscopic Quantum Experiments, by Chunnong Zhao and et al.. The earlier version of the paper was posted in arXiv:0710.2383v3, which didn’t investigate the phase noise in detail and was already cited in my paper.

Several interesting papers in the last months

It has been for a long time since my last post on quantum physics. Here I select some interesting papers on cavity and optomechanics.

One most interesting paper I read in the last month is from Prof. Vahala and Prof. Painter’s groups. They demonstrated that micro-mechanical oscillator can be driven and cooled by the optical gradient force, other than traditional scattering radiation pressure. This approach makes it possible that photon momentum to be transferred over a length scale approaching the wavelength of light. They use double-disk structure, which provides back-action several orders larger than the previous one. They also demonstrate the cooling factor of 13 dB under heavily damped conditions (mechanical Q=4).

Another paper is discussing the proposal for a search for the cosmic axions using an optical cavity.  Axions, which were postulated 30 years ago, remain an attractive candidate for the cold dark matter of the universe. The proposal uses some stokes-like processes to detect the axions. The axions are absorbed by an optical cavity field of frequency . The sidebands appear on the carrier. The displacement of the sidebands is the axion frequency . The proposal is very sensitive.

The last one is discussing the possibility of realizing the strong coupling between a mechanical oscillator and a single atom, from Prof. Kimble’s group. The strong coupling between a cavity mode and a single atom has been accomplished for about 10 years. Once the strong coupling between a mechanical oscillator and a single atom was realized, there are countless application the the technique. Everything you have done in the Cavity-QED systems can be transferred to the optomechanical plus atomic systems. It allows us to coherent manipulation, preparation and measurement  of micromechanical objects.

New paper!

Generating EPR beams in cavity optomechanical system

Authors: Zhang-qi Yin, Y.-J Han

Abstract: We propose a scheme to produce continuous variable entanglement between phase-quadrature amplitudes of two light modes in optomechanical system. For proper driving power and detuning, the entanglement is insensitive with bath temperature and Q of mechanical oscillator. Under realistic experimental conditions, we find that the entanglement could be very large even at room temperature.

You can read it in arXiv:0811.0424.

Update: the paper has been published in Phys. Rev. A 79, 024301 (2009).

Normal life started

I have been in USA for a month. I have to say in the last month, my life is not normal. It is different and excited.

Many of people say that there is a culture shock when you enter the different country. I have felt it, though not very intensive. I have to cook myself and lease a apartment once I entered USA. This is totally different life style. I need some time to suit it. Every day I get up in 9:00 am. After breakfast, I go to lab by AATA bus. Around 6:00 pm, I go back home by bus or feet. Every week, I will come to supermarket buy food and other things. Buying food once a week (or two), this is standard American life.

In the apartment, there is no desk and chair and bed. I have to buy it myself. In fact, I only get dinning desk and sofa up to now. So the life in the home is a little tough. For many days, I sleep on the mattress, open my eyes and think something or nothing. Time is killed like this.

Yesterday, internet was OK in my apartment. I feel my normal life comes back. Now the only thing I need to do is buying laptop.

In U of Mich Now

I came to USA in Sep 23. Now I am in U of Michigan. There are lot of works I must do. I must lease house, complete paper works, check in in International center and my department, and so on. Ann Arbor is a beautiful smal town. Life here is very simple, especially for researchers. When I have my notebook computer and house, I will return to blog.

New paper is available now, arXiv:0704.0482

Implementation of holonomic quantum computation through engineering and manipulating environment

Zhang-qi Yin, Fu-li Li and Peng Peng

We consider an atom-field coupled system, in which two multilevel atoms are respectively trapped in two distant cavities which are connected by an optical fiber and are shined by a broadband squeezed light. We show that a two-qubit geometric CPHASE gate between the two atoms can be implemented through adiabatically manipulating the squeezed reservoir along a closed loop. The scheme has two remarkable features. First, no matter how small but nonzero the squeezing amplitude is, a CPHASE gate with arbitrary phase shift can always be implemented. Second, in contrast to previous quantum computation schemes, the larger the effective coupling strength between the environment and the atoms is, the more reliable the realized CPHASE gate is.

In this work, we investigate the possiblility of realizing quantum computation via steering environment, other than controlling Hamiltonian of the quantum systems themselves or choosing measurement strategy. Let me briefly explain our motivation on doing this work.

When building future quantum computer, we must investigate practical systems which could be divided into three subsystems, which are quantum systems, quantum environments and detectors. Up to now, to our knowledge, there are two different types of schemes, controlling the Hamiltonian of quantum systems themselves (see Cirac and Zoller’s paper in 1995) and choosing measurement strategy (such as one-way quantum computer). So it would be interesting to investigate whether it is possible to realize quantum logic gate, such as a two-qubit CPHASE gate, via manipulating quantum environment. Our work reveals this possibility. Therefore, combining our resualts with previous works, we get following insights: Hamiltonians of the quantum systems, environment where quantum systems place and detectors which measure quantum systems, each of them could be manipulated to realize quantum compution.

I believe this work makes our understanding on realizing quantum computation and quantum control more deeply. In doing this work, we got valueable suggestions from Xiao Yun-feng (USTC). I also thank Star Forum where I got valueable suggestions.

Quantum origin of quantum jumps, perfect lens

In the paper “Quantum origin of quantum jumps: Breaking of unitary symmetry induced by information transfer and the transition from quantum to classical“, M. H. Zurek discussed origin of quantum jumps. He showed how to derive the collapse postulate when a transfer of information essential for both measurement and decoherence is modeled as unitary quantum porcess. The paper contains fruitful ideas and is very easy to read.

As PhysicsWeb reported, two groups in USA showed how to realize sub-wavelength lens through negative refraction materials. Their works reveal the possibility of optical imaging proteins, viruses and DNA, because in principle, the negative refraction lens can rsolve objects only a few nanometers across. I have no idea on negative refraction materials. But I think it is cool! So I download the papers and plan to read it thoroughly.

Slow measurement in quantum computation

In “Effective Fault-Tolerant Quantum Computation with Slow Measurements“, David P. DiVincenzo and Panos Aliferis discussed a very important problem in fault-tolerant quantum computation, does the speed of measurement influences the quantum accuracy threshold greatly? As all investigation on the threshold was based on fast measurement, which is no longer than a few gate operation times, they considered the slow measurement case, that is a measurement takes 1000 gate operations. They found that the slow measurement has a very minimal effect on the quantum accuracy thresold. Their results may be a good news for solid-state quantum computing, where the measurement canot be as short as gate operation times.

Ultrahigh quality cavities

Recently, two groups reported their progresses in manipulating ultrahigh Q cavities.

Ivan S. Grudinin et al. demonstrated a record quality factor of (6.3 pm 0.8) times 10^10 in crystalline whispering gallery mode resonator, corresponding to cavity ring-down time of tau approx 36 {mu}s. They found for a 100 {mu}m LiNbO3 cavity, a single photon would shift the cavity resonance by as much as 6 Hz. Such shift could be detected with optical techniques. This allows the quantum nondemoliion measurement for the number of photons in a cavity. I hope the shift can be enlarged in future. If the shift is large enough, this resonator may be used as a device to entangle photon qubits.

S. Kuhr et al. built a Fabry-Perot supeconducting resonator with quality factor Q = 4.2 times 10^10 and finesse 4.6time 10^9. The demping time T_c of the cavity is as long as 130 ms at resonante frequency 51 GHz and temperature 0.8 K. In previous experiments, T_c was limited to 1 ms. The field damping time of their cavity is 100 times longer than previous ones. I think this microwave F-P resonator is very powerful for realizing quantum information processes. The coupling strength g between atom and cavity is about 310 kHz, which is 4 orders larger than cavity decay rate. As I discussed before, realizing a entangling gate in this system only requires time of 1.7/g, and realizing a nearly perfect controlled-Z gate only needs 3.4/g.. Therefore, the effects of cavity damping can be neglected. Besides, for Rydberg atoms with quantum number 51 and 50, the spontaneous emission rate is of the order 10^2 which is 3 orders lower than time needed in quantum processes. Therefore, a almost perfect quantum logic gate (with fidelity larger than 0.99) may be realized in this cavity.

Spin Hall effects, teleporatation, foundation of statistical mechanics

Spin Hall effects for cold atoms in a light induced gauge potential in cond-mat/0607127, Shi-Liang Zhu et al. proposed a scheme to observe spin Hall effects with cold atoms in a light induced gauge potential. They shown that their scheme was practical and discussed the SHE in an optical lattice.
My comments: It is a very nice and simple scheme. I found it readable for me even though I know little about SHE.

Quantum teleportation between light and matter in Nature 443, 557-560 (5 October 2006), Jacob F. Sherson et al. archieved the teleportation between light and matter. The distance between transmitter and reciever is 0.5m. The fidelity of the teleportation is 0.6. This is a very important step for realizing quantum network.

Entanglement and the foundations of statistical mechanics in Nature Physics 2, 754 – 758 (2006), Sandu Popescu, Anthony J. Short and Andreas Winter argue that the foundations of the statistical mechanics is misleading. The main postulate of statistical mechanics, the equal a priori probability postulate, should be replace by a general canonical principle. They mathimatically proved the general canonical principle. Seth Lloyd wrote a views on the article in Nature Physics.

Entanglement surviving and Mechanical qubit

Quantum interference and evolution of entanglement in a system of three-level atoms in quant-ph/0606182, L. Derkacz and L. Jakobczyk from IFT of Uniwersytet Wroclawski consider the disentanglement of a pair of V-type atoms due to the spontaneous emission and quantum interference between principal transitions in this process. An interesting result they find is that some part of intial entanglement can survive in the limit of maximal interference. My comments: This result is closely related with other two papers: quant-ph/0604020, quant-ph/0605033. In those papers, it was found that atoms can be entangled by environment, which can be called “dissipation induced entanglement effect“. In my opinion, all these three papers can be explained by the Decoherence-free subspace theory.

Quantum electromechanics: qubits from buckling nanobars, in New J. Phys. 8 105. Sergey Savel’ev and Xuedong Hu and Franco Nori ” propose a mechanical qubit based on buckling nanobars”. “The fascinating prospect of observing quantum coherent phenomena in a macroscopic mechanical oscillator is a main motivation of this study.” This work is interesting as it shows the possibility of implement mechanical quantum information processors. “This would be an ironic turn of events, given that the first computers (by C Babbage) were mechanical.”

Recent papers in my eyes

I will begin to write entries about the recent interesting papers in the quantum information and related fields. I plan to write brief summary for each paper, just as Coherence* does. I will use English in these entries for which is more popular among researchers. I apologize for the guests who are unfamillar with English and the jargons in quantum information. If the paper is very important, I will write an entry to discuss it in two language: English and Chinese. I must emphasise that these papers are only interesting for me, and the entries are based on personal opinions. If you have different opinions, please leave your comments.

Controllable coupling between qubits

Switching on/off the interactions between qubits is vital in realising quantum computation. Here I list three papers I read recently on this subject.

1. S. F. Yelin et al., quant-ph/0602030. In this article a new platform – altracold polar molecules – for quantum computing with switchable interactions was proposed. The on/off switch is realised by selectively exciting “0″ or “1″ qubits to excited state with considerably different dipole moment.
2. Ming-Yong Ye et al.. In this article, to realising solid-state quantum computation, practical pulses can be used for controlling interactions and the global magnetic field.
3. Yu-xi Liu et al.. An experimentally realizable method to control the coupling between two flux qubits was proposed in this article.

Though these methods are different and related to different physical system, changing Hamiltonian is needed in all of them. Can we control the interaction between the qubits only by local operations on the qubits?

At home at last

I arived at home yesterday at last, after almost one day and one night training. The most terrible thing in the world is going home by train in China during spring fesitavel time. My train was late for 6 hours when it arived at the station of my hometown. The reason is following numbers:

• 3.6 million people went home by train yesterday in China.
• Tens of hours strong snowing in Henan province yesterday.
• Two main railways in China was out of runing because of snowing.

Luckily, my hometown is not snowing and not very cold. How fragile railways in China!

How to detect entanglement

As we know, entanglement is the most important resource in quantum information, quantum computation, et al. If we have got all the information of the system and can write down its state, we can use many criterions to judge whether the system is entangled or not. The most useful criterion is the “Peres criterion”. But in the laboratory it is very difficult to get all the information of the system. In this limited condition, how can we detect entanglement?

The physicist’s logic is very simple. In principle only Hermite physical quantity is measurable. For example susceptibility is measurable. If we can find some physical quantity that must be fulfilled some condition if the system is separable, we can use it to detect the entanglement. This quantity is called entanglement witness.

To get the condition of entanglement, uncertainty relation and Schwarz inequality should be used together with the definition of the separable state. Most of the witness are the variance of some quantity which could be detected directly. But no witness is good enough to detect all entanglement. For example, it is very difficult to detect the entanglement of the Bell state through entanglement witness. Many new witness will be introduced to improve detection efficient and detect more entangled states.