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{{quantum mechanics}}
'''Circuit quantum electrodynamics''' ('''circuit QED''') provides means to study the fundamental interaction between light and matter. As in the field of [[cavity quantum electrodynamics]], a single photon within a single mode [[optical cavity|cavity]] coherently couples to a quantum object (atom). In contrast to cavity QED, the photon is stored in a one-dimensional on-chip resonator and the quantum object is no natural atom but an artificial one. These [[artificial atom]]s usually are mesoscopic devices which exhibit an atom-like energy spectrum.
The field of circuit QED is a prominent example for [[quantum information science|quantum information processing]] and a promising candidate for future [[quantum computer|quantum computation]].<ref>{{cite journal|author=Alexandre Blais ''et al.''|year=2004|title=Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computing|journal=[[Physical Review A|Phys. Rev. A]]|volume=69|pages=062320|publisher=[[American Physical Society|APS]]|doi=10.1103/PhysRevA.69.062320}}</ref>


== Resonator ==
The resonant devices used for circuit QED are [[superconductivity|superconducting]] [[coplanar waveguide]] [[microwave]] resonators,<ref>{{cite journal|author=M. Göppl ''et al.''|year=2008|title=Coplanar waveguide resonators for circuit quantum electrodynamics|journal=[[Journal of Applied Physics|J. Appl. Phys.]]|volume=104|pages=113904|publisher=[[American Institute of Physics|AIP]]|doi=10.1063/1.3010859}}</ref> which are two-dimensional microwave analogues of the [[Fabry–Pérot interferometer]]. Coplanar waveguides consist of a signal carrying centerline flanked by two [[ground (electricity)|grounded]] planes. This planar structure is put on a dielectric substrate by a photolithographic process. [[superconductivity|Superconducting]] materials used are mostly [[aluminium]] (Al) or [[niobium]] (Nb). Dielectrics typically used as substrates are either surface oxidized [[silicon]] (Si) or [[sapphire]] (Al<sub>2</sub>O<sub>3</sub>).
The [[characteristic impedance|line impedance]] is given by the geometric properties, which are chosen to match the 50 <math>\Omega</math> of the peripheric microwave equipment to avoid partial reflection of the signal.<ref>{{cite book|last=Simons |first=Rainee N. |title=Coplanar Waveguide Circuits, Components, and Systems |publisher=John Wiley & Sons Inc. |year=2001 |isbn=0-471-16121-7}}</ref>
The electric field is basically confined between the center conductor and the ground planes resulting in a very small mode volume <math>V_m</math> which gives rise to very high electric fields per photon <math>E_0</math> (compared to three dimensional cavities).


<math>E_0=\sqrt{\frac{\hbar\omega_r}{2 \varepsilon_0 V_m}}</math>
Sam's Club is trying to stand out against its larger, faster-growing  [http://tinyurl.com/kecvhhb http://tinyurl.com/kecvhhb] rival Costco Wholesale Corp (COST.O) with trendier  [http://tinyurl.com/kecvhhb ugg boots sale] holiday merchandise this year, hoping that new goods will spur its members to spend more.<br>Its previous moves, including improving food and adding "treasure hunt" items such as $6,000 Cartier watches, have failed to spur strong results. Sales and the growth trajectory at the retail warehouse chain, part of Wal-Mart Stores Inc (WMT.N), continue to lag behind Costco.<br>"We've been underwhelming our members," Chief Executive Officer Rosalind Brewer said as she toured a new Sam's Club in Romeoville, Illinois, last week. Some goods just have not been "on trend" enough, she said.<br>When Wal-Mart meets with analysts and investors on October 15, Brewer will give more details about the merchandising strategy for Sam's Club, a membership-only retailer.<br>The chain is adding 132  [http://tinyurl.com/kecvhhb discount ugg boots] new general merchandise goods for the holiday season, up from 56 a year ago. They include everything from sets of "heirloom" Christmas ornaments that look like ones sold in boutiques, to women's [http://tinyurl.com/kecvhhb cheap ugg boots] [http://tinyurl.com/kecvhhb cheap ugg boots] priced below the $200 or more they sell for at department stores.<br>Sam's Club has lacked a bit of the "flair" that Costco has, said Wolfe Research analyst Scott Mushkin. Adding new items may help but could be more of an "incremental positive" rather than really moving the needle, he said, without seeing the goods.<br>Costco has not changed its holiday strategy and is keeping an eye on its rival, Chief Financial Officer Richard Galanti said on October 9. Sam's Club's [http://tinyurl.com/kecvhhb discount ugg boots] booklets, launched months ago, are similar to ones Costco has used for years.<br>"We are going to do what we do," Galanti said on a conference call. "If they keep doing it, it must be working."<br>Sales at stores open at least a year, a retail metric known as same-store sales, show that Costco has an edge. Costco's U.S. same-store sales rose 5 percent last quarter. Sam's Club's same-store sales rose 1.7 percent last quarter and it expects them to be flat to up 2 percent this quarter.<br>"The results have not been consistently barn burning while Costco's have," said Cowen & Co analyst Faye Landes. In the past, Sam's Club's formula has not seemed to be "quite as nailed down as Costco's," she said.<br>Sam's Club, which has 627 warehouses in the United States and Puerto Rico and is opening 15 to 20 more a year, declined to forecast sales or profit margins on the new items. Costco runs 638 warehouses, including 454 in the United States and Puerto Rico, and plans to open 18 more U.S. ones this fiscal year.<br>Sam's Club, which got its start in Oklahoma 30 years ago, has been trying to stand out as a warehouse of brand names. It is the only club to sell Apple Inc (AAPL.O) devices and also stocks items such as The North Face fleece jackets from VF Corp (VFC.N) and Under Armour Inc (UA.N) shirts.<br>It hopes to lure members like Sue Skeer to spend more. Skeer said she joined Sam's Club 16 years ago and goes there about twice a week, mainly to buy fruits and vegetables.<br>"I haven't really found anything that would draw me in" to make many impulse purchases, said Skeer, who lives in Granite Bay, California.<br>(Reporting by Jessica Wohl; editing by Andrew Hay)<br>Tweet this <br>Link this <br>Share this<br>Digg this <br>Email<br>Print<br>Reprints<br>We welcome comments that advance the story through relevant opinion, anecdotes, links and data. If you see a comment that you believe is irrelevant or inappropriate, you can flag it to our editors by using the report abuse links. Views expressed in the comments do not represent those of Reuters. For more information on our comment policy, see website Comments (1) OkHank wrote: I�ve been a Sams club member for 21 years. It is sad they have dropped there �In business for small business� format now it�s be a Plus Member and throw the business under the bus. I have had no choice like many other businesses over the years to purchase from a food service. It amazing to me they don�t understand the dollars lost over all my personal example in 2004 I was spending 300k a year 2007 200k and now 2013 lucky to spend 40 - 50k that said were doing 4X the business now than in 2004<br>
 
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One can distinguish between two different types of resonators: <math>\lambda/2</math> and <math>\lambda/4</math> resonators. Half-[[wavelength]] resonators are made by breaking the center conductor at two spots with the distance <math>\ell</math>. The resulting piece of center conductor is in this way [[capacitor|capacitively]] coupled to the input and output and represents a resonator with <math>E</math>-field [[antinode]]s at its ends. Quarter-wavelength resonators are short pieces of a coplanar line, which are shorted to ground on one end and capacitively coupled to a [[feed line]] on the other. The resonance frequencies are given by
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<math>\lambda/2: \quad \nu_n=\frac{c}{\sqrt{\varepsilon_{\text{eff}}}}\frac{n}{2 \ell} \quad (n=1,2,3,\ldots) \qquad \lambda/4:\quad  \nu_n=\frac{c}{\sqrt{\varepsilon_{\text{eff}}}}\frac{2n+1}{4 \ell} \quad (n=0,1,2,\ldots)</math>
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with <math>\varepsilon_{\text{eff}}</math> being the effective dielectric [[permittivity]] of the device.
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== Artificial atoms, Qubits ==
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The first realized artificial atom in circuit QED was the so called Cooper-pair box.<ref>{{cite journal|author=A. Wallraff ''et al.''|year=2004|title=Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics|journal=[[Nature (journal)|Nature]]|volume=431|pages=162–167|publisher=[[Nature Publishing Group]]|doi=10.1038/nature02851|issue=7005|pmid=15356625}}</ref> In this device, a reservoir of [[cooper pair|Cooper-pairs]] is coupled via [[josephson effect|Josephson junctions]] to a gated superconducting island. The state of the Cooper-pair box ([[qubit]]) is given by the number of Cooper pairs on the island (<math>N</math> Cooper pairs for the ground state <math>\mid g \rangle</math> and <math>N+1</math> for the excited state <math>\mid e \rangle</math>). By controlling the [[electric potential energy|Coulomb energy]] ([[biasing|bias voltage]]) and the [[Josephson energy]] (flux bias) the transition frequency <math>\omega_a</math> is tuned. Due to the nonlinearity of the Josephson junctions the Cooper-pair box shows an atom like energy spectrum.
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Other more recent examples for qubits used in circuit QED are so called [[transmon]] qubits <ref>{{cite journal|author=Jens Koch ''et al.''|year=2007|title=Charge insensitive qubit design derived from the Cooper pair box|journal=[[Physical Review A|Phys. Rev. A]]|volume=76|pages=042319|publisher=[[American Physical Society|APS]]|doi=10.1103/PhysRevA.76.042319}}</ref> (more charge noise insensitive compared to the Cooper-pair box) and flux qubits (the state is given by the direction of a supercurrent in a superconducting loop intersected by Josephson junctions).
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All of these devices feature very large dipole moments <math>d</math> (up to 10<sup>3</sup> that of large <math>n</math> [[Rydberg atom]]s), which qualifies them as extremely suitable coupling counterparts for the light field in circuit QED.
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== Theory ==
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The full quantum description of matter-light interaction is given by the [[Jaynes-Cummings model]].<ref>{{cite journal|author=E. T. Jaynes and F. W. Cummings|year=1963|title=Comparison of Quantum and Semiclassical Radiation Theories with Application to the Beam Maser|journal=[[Proceedings of the IEEE]]|volume=51|pages=89–109|publisher=[[Institute of Electrical and Electronics Engineers|IEEE]]}}</ref> The three terms of the Jaynes-Cummings model can be ascribed to a cavity term, which is mimicked by a harmonic oscillator, an atomic term and an interaction term.
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<math> \mathcal{H}_{\text{JC}}=\underbrace{\hbar \omega_r \left(a^\dagger a+\frac 12\right)}_{\text{cavity term}}+\underbrace{\frac 12 \hbar \omega_a \sigma_z}_{\text{atomic term}}+\underbrace{\hbar g \left(\sigma_+ a+a^\dagger \sigma_-\right)}_{\text{interaction term}}</math>
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In this formulation <math>\omega_r</math> is the resonance frequency of the cavity and <math>a^\dagger</math> and <math>a</math> are photon creation and annihilation operators, respectively. The atomic term is given by the [[Hamiltonian (quantum mechanics)|Hamiltonian]] of a spin 1/2 system with <math>\omega_a</math> being the transition frequency and <math>\sigma_z</math> the [[pauli matrices|Pauli matrix]]. The operators <math>\sigma_\pm</math> are raising and lowering operators ([[ladder operator]]s) for the atomic states.
Chi<br><br>
For the case of zero detuning (<math>\omega_r=\omega_a</math>) the interaction lifts the degeneracy of the photon number state <math>\mid n \rangle</math> and the atomic states <math>\mid g \rangle</math> and <math>\mid e \rangle</math> and pairs of dressed states are formed. These new states are [[quantum superposition|superpositions]] of cavity and atom states
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<math>\mid n,\pm \rangle=\frac 1{\sqrt 2}\left(\mid g\rangle \mid n \rangle\pm \mid e\rangle \mid n-1\rangle\right)</math>
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Ita<br><br>
and are energetically split by <math>2g\sqrt n</math>.
Jap<br><br>
If the detuning is significantly larger than the combined cavity and atomic [[spectral linewidth|linewidth]] the cavity states are merely shifted by <math>\pm g^2/\Delta</math> (with the detuning <math>\Delta=\omega_a-\omega_r</math>) depending on the atomic state. This provides the possibility to read out the atomic (qubit) state by measuring the transition frequency.
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The coupling is given by <math>g=E \cdot d</math> (for electric dipolar coupling). If the coupling is much larger than the cavity loss rate <math>\kappa=\frac{\omega_r}Q</math> (quality factor <math>Q</math>; the higher <math>Q</math>, the longer the photon remains inside the resonator) as well as the decoherence rate <math>\gamma</math> (rate at which the qubit relaxes into modes other than the resonator mode) the strong coupling regime is reached. Due to the high fields and low losses of the coplanar resonators together with the large dipole moments and long decoherence times of the qubits, the strong coupling regime can easily be reached in the field of circuit QED. Combination of the Jaynes–Cummings model and the coupled cavities leads to the [[Jaynes-Cummings-Hubbard model]].
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Latest revision as of 06:44, 28 September 2014


Sam's Club is trying to stand out against its larger, faster-growing http://tinyurl.com/kecvhhb rival Costco Wholesale Corp (COST.O) with trendier ugg boots sale holiday merchandise this year, hoping that new goods will spur its members to spend more.
Its previous moves, including improving food and adding "treasure hunt" items such as $6,000 Cartier watches, have failed to spur strong results. Sales and the growth trajectory at the retail warehouse chain, part of Wal-Mart Stores Inc (WMT.N), continue to lag behind Costco.
"We've been underwhelming our members," Chief Executive Officer Rosalind Brewer said as she toured a new Sam's Club in Romeoville, Illinois, last week. Some goods just have not been "on trend" enough, she said.
When Wal-Mart meets with analysts and investors on October 15, Brewer will give more details about the merchandising strategy for Sam's Club, a membership-only retailer.
The chain is adding 132 discount ugg boots new general merchandise goods for the holiday season, up from 56 a year ago. They include everything from sets of "heirloom" Christmas ornaments that look like ones sold in boutiques, to women's cheap ugg boots cheap ugg boots priced below the $200 or more they sell for at department stores.
Sam's Club has lacked a bit of the "flair" that Costco has, said Wolfe Research analyst Scott Mushkin. Adding new items may help but could be more of an "incremental positive" rather than really moving the needle, he said, without seeing the goods.
Costco has not changed its holiday strategy and is keeping an eye on its rival, Chief Financial Officer Richard Galanti said on October 9. Sam's Club's discount ugg boots booklets, launched months ago, are similar to ones Costco has used for years.
"We are going to do what we do," Galanti said on a conference call. "If they keep doing it, it must be working."
Sales at stores open at least a year, a retail metric known as same-store sales, show that Costco has an edge. Costco's U.S. same-store sales rose 5 percent last quarter. Sam's Club's same-store sales rose 1.7 percent last quarter and it expects them to be flat to up 2 percent this quarter.
"The results have not been consistently barn burning while Costco's have," said Cowen & Co analyst Faye Landes. In the past, Sam's Club's formula has not seemed to be "quite as nailed down as Costco's," she said.
Sam's Club, which has 627 warehouses in the United States and Puerto Rico and is opening 15 to 20 more a year, declined to forecast sales or profit margins on the new items. Costco runs 638 warehouses, including 454 in the United States and Puerto Rico, and plans to open 18 more U.S. ones this fiscal year.
Sam's Club, which got its start in Oklahoma 30 years ago, has been trying to stand out as a warehouse of brand names. It is the only club to sell Apple Inc (AAPL.O) devices and also stocks items such as The North Face fleece jackets from VF Corp (VFC.N) and Under Armour Inc (UA.N) shirts.
It hopes to lure members like Sue Skeer to spend more. Skeer said she joined Sam's Club 16 years ago and goes there about twice a week, mainly to buy fruits and vegetables.
"I haven't really found anything that would draw me in" to make many impulse purchases, said Skeer, who lives in Granite Bay, California.
(Reporting by Jessica Wohl; editing by Andrew Hay)
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We welcome comments that advance the story through relevant opinion, anecdotes, links and data. If you see a comment that you believe is irrelevant or inappropriate, you can flag it to our editors by using the report abuse links. Views expressed in the comments do not represent those of Reuters. For more information on our comment policy, see website Comments (1) OkHank wrote: I�ve been a Sams club member for 21 years. It is sad they have dropped there �In business for small business� format now it�s be a Plus Member and throw the business under the bus. I have had no choice like many other businesses over the years to purchase from a food service. It amazing to me they don�t understand the dollars lost over all my personal example in 2004 I was spending 300k a year 2007 200k and now 2013 lucky to spend 40 - 50k that said were doing 4X the business now than in 2004
Many business members are disappointed the direction they have taken. But on a happier note Costco is coming to town!
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