Monthly Archives: January 2011

Properties of Matter

First class of Chemistry 131.

There are two types of matter. Mixtures and Pure. The difference between the two is that mixtures can be physically separated, while pure substances can be chemically separated if at all.

Mixtures can be Homo(geneous) or Hetro(geneous). Homo’s are uniform throughout, and Homo’s do not contain the Tyndall effect. The Tyndall effect is the reflection of light off of the small particles suspended in the mixture. For example, it becomes harder to see through fog when the high beams are on. Hetro’s are an uneven distribution of particles, and contains two sub-categories, Colloids and Suspensions. Colloids, which consist of medium size particles and display the Tyndall effect, the particles don’t settle. An example of a colloid is Milk. Suspensions are made from large particles, show the Tyndall effect and the particles settle out. For example, lemonade.

Physical Separation Systems:

Pure substances are either Compounds or Elements. Compounds are chemically separable and break down into elements. Compounds contain a fixed ratio of elements. Compounds and elements have a definite make-up (composition?) and properties Compounds are two or more kinds of atom’s that are bonded. (Each element is a type of atom) Mixtures are two or more Compounds.  (Can a mixture consist of two elements as long as it is physically separable?) IE gold and silver beads, mixed together.

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Quantum Computing: Origins and Directions

A presentation by David DiVincenzo sponsored by Research Laboratory of Electronics at MIT

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Reading “Slowing and stopping light using an optomechanical crystal array”

Slowing and stopping light using an optomechanical crystal array” from the Institute for Quantum Information at Caltech, is about an idea for storing information as light, by slowing the light. (Can light travel slower than the speed of light?) Right now optical networks have to transition to an electrical signal to store information. There are several different schemes already under consideration for how to do this, and the approach taken in this paper combines many of their features.

The scheme used in this paper involves mapping the optical field into mechanical excitations. The mechanical excitations are created on an optomechancial crystal array. Directly quoting the authors an optomechanical crystal is “a periodic structure that constitutes both a photonic and a phononic crystal.” Photonic crystals are composed of patterns regions of high and low dielectric constants. Phononic crystals are patterns of regions of elasticity and mass. Photonic crystals are light based and phononic crystals are sound based.

The optomechanical crystal works by transferring the cavity mode of an optical cavity to the mechanical mode of the crystal. The cavity mode comes from an optical waveguide that is coupled to it. The optical modes leak energy into the waveguide and have a decay rate as well. There is a driving amplitude of Capital omega for a single optical cavity system. A Hamiltonian is used to describe the dynamics of a single element, depending on whether or not the system has one or two optical cavities, the Hamiltonian contains the optomechanical driving amplitude (for single cavity).

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Thoughts from reading “Decoherence of floating qubits due to capacitive coupling”

Link: Decoherence of floating qubits due to capacitive coupling.

I decided to read this paper because I saw a link to a different paper by the same author on the Caltech course website. I looked up the author and chose this paper because the qubit is floating.

Electrically floating qubits (floating flux qubits)  are one of the possible superconducting qubits for constructing gates in a quantum computer. The decoherence time of flux qubits is not as high as was expected. A higher decoherence time was expected because since the qubit is floating it is not in contact with ground.  The reason for the shorter decoherence time is that the reactance of the capacitance to the ground increases for frequencies in the microwave range, even though it is not touching the ground. To limit the short decoherence time, the qubit’s should be symmetrically coupled to bias leads. Then the admittance of the bias leads should be adjusted. Admittance is the inverse of the opposition to alternating current.

To show symmetrically coupled qubit’s are a better option a simulation of a RF SQUID is created. An RF SQUID is a “Radio Frequency Superconducting Quantum Interference Device”. The first example is of an RF SQUID using a capitance connected to ground and to a bias lead. The decoherence time is short for this example. The second example is connected to two bias leads. Then in a thought experiment one of the lead’s is removed and a current loops in either one direction or the other, depending on which lead was removed. Meaning when both lead’s are connected the current is zero.

Josephson Junction: Two superconductors separated by a very thin non-conducting film. A current still manages to cross, and it is called the Josephson current.

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Thoughts from reading “Creation of a quantum oscillator by classical control”

Creation of a quantum oscillator by classical control

The LIGO gravitational wave observatory uses mirrors as a method to detect gravitational waves. The mirrors are very sensitive to even the slightest disturbance, so reducing exposure to noise is critical for detecting gravitational waves.

SQL: Standard Quantum Limit (not Structured Query Language)

The mirrors are hanging like pendulums and oscillating with a resonant frequency and a damping rate. Electronic feedback control is used to shift the resonant mode upwards and then to damp it. This changed the occupation number. (What is an Occupation Number?)

Occupation Number: The occupation number is used in second quantization: field theory, which is used to describe systems where particles can be created or destroyed.

While reading this paper the capital omega symbol I was unsure of in a previous post (here) is defined. It is the eigenfrequency of the controlled oscillator.

The reason for observing the occupation number is to calculate the “quantum-ness’ of the system. In this case though I think the system is a 10 kg mirror, which is not what I think of when I hear ‘quantum system’. I’m not sure why, but this time occupation number is not an ideal measure of quantum-ness (Is it because the system is non-standard?). Instead they look at the purity, which is composed of the uncertainties of the oscillators position, momentum and the interrelation between the two. The purity is used to calculate a minimum occupation number and determine a value for an arbitrary eigenfrequency.

To rephrase the last sentence, “The eigenfrequency is a function of the minimum occupation number”. Depending on where or not the eigenfrequency is greater or less than lower case omega (I think it’s angular frequency here) the quantum state is either position squeezed or momentum squeezed. (Squeezed?)

The remainder of the paper (pages 2 –  4) are about how to use the calculated eigenfrequency to devise an optimal controller to be used for frequency of the oscillator.

There are several references to Markovian measurements, what makes a measurement Markovian?

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Notes on “Parallel State Transfer and Efficient Quantum Routing on Quantum Networks”

The paper “Parallel State Transfer and Efficient Quantum Routing on Quantum Networks” describes a theoretical model for the routing of quantum information in parallel on multi-dimensional networks. Routing on a multi-dimensional network can be used for the transfer of entanglement. (What is a multi-dimensional network? Is it the number of interconnected nodes? For instance, one node connected to three others, is that 3-d? Is 8 nodes all wired to each other an 8-d network?)

There are two conditions for efficient routing:

1.     Quantum states must be transferable between arbitrary nodes.

2.     The network should be able to transfer states between nodes in parallel.

A quantum network is made up of nodes. Each node is an oscillator with a tunable frequency. Different arrangements of coupling between oscillators with the same frequency and couplings between oscillators with different frequencies lead to different network schemes.  

The paper considers parallel quantum networks by first considering the fidelity of parallel state transfer and next evaluating different entanglement distribution schemes. The fidelity of parallel state transfer shows that multiple nodes can accurately send entanglement through the network at the same time. This is important, because it allows for more entanglement schemes. An entanglement distribution scheme is the method of interconnection used in the network. Similar to how in a classical network, all of the nodes can take to each other, or one node can talk to the node before and after it etc… there are a variety of classical network schemes.

To begin the description of the network, it is described mathematically as a graph which is a function of vertices and edges, with a Hamiltonian that describes the frequencies of each node. Each node must be tunable, so it could be set to a particular frequency.

The next step is the analysis of the transfer of entanglement between nodes.  This is considered first as a process and then as a time-evolution of the initial state. Thinking about the transfer of entanglement as a time-evolution of the initial state allows for additional analysis, like calculating the fidelity of the final density. 

Next parallel state transfer on a hypercube is considered. This is confusing to me, because the symbol capital omega, which I thought was being used to describe the frequency of each node is now being used to describe a coupling matrix. The coupling matrix is used to calculate the fidelity of the parallel state transfer, for qubit or oscillator networks. This is still on a hypercube though. By expanding parallel state transfer to a complete graph, the network becomes massively parallel. I think massively parallel means all nodes can send and receive with each other. This makes Fidelity not dependent on the number of nodes. The new calculation for the distribution rate is much faster.

Finally the effects of decoherence are briefly covered. Decoherence will reduce the performance of the network, and further study is needed to see the effects on the massively parallel scheme.

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Reading Notes on  “Cavity optomechanics using an optically levitated nanosphere”

Notes on Cavity optomechanics using an optically levitated nanosphere” by D.E. Chang, C.A. Regal, S.B. Papp, D.J. Wilson, J. Ye, O. Painter, H.J. Kimble, P. Zoller

The reason for optically levitating a nanosphere is to minimize contact of other materials with the sphere, so that the sphere can be kept cold, with less effort. This means quantum effects can be observed for a longer time.

The paper talks about reducing thermalization and decoherence rates of nano and micro-mechanical systems. Thermalization is the process of returning the temperature to equilibrium and decoherence is the appearance of wave function collapse, (decoherence post) The reason to reduce these two things is to study whether or not quantum coherence and entanglement can be observed at mesoscopric or macroscopic scales. Mesoscipic is the size range between atomic and macroscopic.

When a sphere is optically levitated in a vacuum, it can be cooled, and quantum behavior emerges even in room temperature environments.  (The paper say’s the CM can be self-cooled to the ground state. How does self-cooling work?) Since the CM has a long coherence time, more exotic quantum states can be observed. The paper gives two states. One exotic state is to map a squeezed motional state onto light leaving the cavity. (What is initially squeezed? The sphere?) The other state is to show entanglement originally shared between two modes of light can be transferred onto the motion of two spheres trapped in spatially separate cavities, creating EPR correlations. (EPR post)

The main point of the paper is to talk about the mechanics of the CM of the sphere. I do not know what exactly the sphere is made out of, but the radius of the sphere is much less than the wavelength of the optical modes that are levitating it.  The sphere is like a point dipole. The first thing to do is to optically levitate the sphere. This is done using two standing-wave optical modes. One mode provides an optical dipole trap for the sphere (The sphere is dielectric). The second mode is weaker and has a non-zero intensity gradient at the center of the trap.  The non-zero intensity gradient cools the sphere.

The sphere has a dipole moment and optical potential. The position of the point is the center of mass. It has a polarizability, volume and density. Epsilon, the electric permittivity affects the sphere. The optical field has field intensity.  I think the sphere is oscillating back and forth slightly in the trap. The trap depth is a function of intensity, volume and the real part of electric permittivity. The oscillation frequencies are a function of the wave number, intensity, density and the real part of electric permittivity.  The sphere is subject to noise forces due to collisions with background gas and momentum recoil from scattered photons. The noise forces lead to warming of the sphere.

(Why does the electric permittivity have a real and imaginary component?)

The collision rate, R, between the sphere and gas molecules, tells about how quickly the sphere will become to warm. It is a function of the radius of the sphere, along with other factors. Because of this the ideal radius for a sphere to levitate can be determined.

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Reading notes on “Coherent population trapping resonances with linearly polarized light for all-optical miniature atomic clocks”

Link to the Paper:

Coherent population trapping resonances with linearly polarized light for all-optical miniature atomic clocks

This paper is about how to make miniature atomic clocks, small enough to fit on computer chips. In particular it is talking about a CPT (coherent population trapping) interaction scheme. CPT is done by using two resonant optical fields and a single diode laser.

Atoms are placed into a superposition of two hyperfine ground states. Once the atoms are in the superposition they are very sensitive and the CPT effect can be used to sense atomic frequencies. Hyperfine defines an atomic energy state resulting from the interactions of the nucleus with internally generated electric and magnetic fields.

CPT resonance provides the best results when the light fields are of the same polarization. Types of polarization are circular, linear and elliptical. The desired angular momentum for the strongest resonance are in states where m = 0.

This paper is an experimental and theoretical study about a particular CPT interaction scheme using alkali metal atoms, and two linearly polarized optical fields. This optical set up is called lin|lin CPT. Alkali metals are: Lithium (Li), sodium (Na), potassium (K), rubidium (Rb), cesium (Cs) and francium (Fr). I think using Alkali metal’s lets the CPT resonance be magneto-insensitive.

The first portion of the paper is a theoretical analysis of the idea. It explains that the hyperfine transition is the change in omega, the angular frequency. This is called the hyperfine splitting.

Usually CPT schemes use circularly polarized optical fields, but this causes a lower density of interacting atoms, because many of the atoms become trapped. Using linear/elliptical polarization permits greater density of interacting atoms. This means a higher CPT resonance. The two formula’s showing the dark state are nearly the same except the non-circular formula has m = +- 1 instead of zero.

Then there is an experimental section. The goal was to produce a resonant bichromatic field, and to do this the output of an external cavity diode laser was externally phase-modulated by and electro-optical modulator. An electro-optical modulator lets the user control the phase of light exiting a crystal based on the electric field the crystal is exposed to, because the refractive index of the crystal changes depending on the strength of the electric field. There are also types that let you control frequency or amplitude.

Once the laser was at a particular frequency it was stabled to a saturation spectroscopy resonance.  The saturation spectroscopy lets the hyperfine transitions within an atom be found. Usually there is a Doppler effect, which makes it difficult to pinpoint the exact transition points. To stabilize the laser a vacuum reference cell was used. I think vacuum reference cells have a drive field and a probe field. What is a vacuum reference cell and what is it doing?

After the light was regulated, it passed through a Rb vapor cell. I think experimental measurements where gathered here, although I’m not sure if measurements where taken right after using a photo detector.  The Rb vapor cell was protected with magnetic shielding and held at a constant temperature.

Throughout the paper there are references to a “Lambda system” (Uppercase) I don’t know what this system means.

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The 14 paper project

The 14 day paper project is similar to an artist’s “Sketch a day” challenge, except instead of drawing a sketch I am reading a paper. Each day I find a journal article at the arXiv archive, read it and write a summary. I am selecting the papers from conversations with Dr Noe, Caltech’s website and summer REU programs from the NSF.

After the 14 days of reading I will go back through my summaries and put together a list of topics to learn more about. The next 7 days will be posts about those topics. 

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