After 60 years: A new formula for computing quality factor is warranted

Feld, David A.; Parker, R.; Ruby, R.; Bradley, P.; Dong, Shim

doi:10.1109/ultsym.2008.0105

Cited by 197 publications

(60 citation statements)

References 6 publications

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“…We calculate the quality factor from the raw data using the method described in [19]. To better estimate the k 2 ef f , the parasitic feed-through pad capacitance is deembedded by measuring open structures with only the probe pads [20] (The de-embedding process only cancels the parastic capacitance, and does not cancel any series routing resistance).…”

Section: Resultsmentioning

confidence: 99%

Design and Fabrication of S<sub>0</sub> Lamb-Wave Thin-Film Lithium Niobate Micromechanical Resonators

Wang

Bhave

Bhattacharjee

2015

J. Microelectromech. Syst.

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Commercial markets desire integrated multifrequency band-select duplexer and diplexer filters with a wide fractional bandwidth and steep roll-off to satisfy the ever-increasing demand for spectrum. In this paper, we discuss the fabrication and design of lithium niobate (LN) thin-film S 0 Lamb-wave resonators on a piezoelectric-on-piezoelectric platform. Filters using these resonators have the potential to fulfill all the above requirements. In particular, we demonstrated one-port highorder S 0 Lamb-wave resonators with resonant frequencies from ∼400 MHz to ∼1 GHz on a black rotated y-136 cut LN thin film. The effective electromechanical coupling factor (k 2 ef f ) ranges from 7% to 12%, while the measured quality factor ranges from 600 to 3300. The highest k 2 ef f × Q achieved on this chip is 194, significantly surpassing contour mode resonators manufactured in other technologies.[2014-0280]

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Section: Resultsmentioning

confidence: 99%

Design and Fabrication of S<sub>0</sub> Lamb-Wave Thin-Film Lithium Niobate Micromechanical Resonators

Wang

Bhave

Bhattacharjee

2015

J. Microelectromech. Syst.

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“…In a companion paper presented at this conference [1], several methods of determining Q are presented and a new method for determining the unloaded Q vs. frequency is given. This new Q equation is based on a theorem derived by Bode [2].…”

Section: Methods Of Determinig Qmentioning

confidence: 99%

“…In that case, errors between eq. 5 and calculations based on the Brute Force Method (BFM) [1] diverge.…”

Section: Methods Of Determinig Qmentioning

confidence: 99%

Method of Extracting Unloaded Q Applied Across Different Resonator Technologies

Ruby

Parker

Feld

2008

2008 IEEE Ultrasonics Symposium

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When comparing different resonator technologies, it is essential that fundamental properties such as the unloaded Q be accurately portrayed. Important Figure-of-Merit (FOM) numbers for resonators include operating frequency, coupling coefficient (kt2), Q, and the products --kt2*Q and f*Q. Three of the five Figure's of Merit depend on an accurate evaluation of unloaded Q. Using a new equation for Q (derived from first principles), we can measure both Q and the coupling coefficient for a variety of resonator technologies and compare the relative performance metrics of each technology.

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“…4 shows a network analyzer measurement of the HBAR admittance (Y 11 ) plotted as a function of frequency. From this frequency comb, we selected the ω mech /2π = 586 MHz resonance mode that has a Q of 2700 as calculated by the Q-circle method [35] and an on-resonance impedance of 18 Ω. This mechanical resonance suppresses driving field amplitude noise that is faster than ω c = ω mech 2Q = 110 kHz.…”

Section: Supplementary Information Device Detailsmentioning

confidence: 99%

Continuous dynamical decoupling of a single diamond nitrogen-vacancy center spin with a mechanical resonator

et al. 2015

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Inhomogeneous dephasing from uncontrolled environmental noise can limit the coherence of a quantum sensor or qubit. For solid state spin qubits such as the nitrogen-vacancy (NV) center in diamond, a dominant source of environmental noise is magnetic field fluctuations due to nearby paramagnetic impurities and instabilities in a magnetic bias field. In this work, we use ac stress generated by a diamond mechanical resonator to engineer a dressed spin basis in which a single NV center qubit is less sensitive to its magnetic environment. For a qubit in the thermally isolated subspace of this protected basis, we prolong the dephasing time T * 2 from 2.7 ± 0.1 µs to 15 ± 1 µs by dressing with a Ω = 581 ± 2 kHz mechanical Rabi field. Furthermore, we develop a model that quantitatively predicts the relationship between Ω and T * 2 in the dressed basis. Our model suggests that a combination of magnetic field fluctuations and hyperfine coupling to nearby nuclear spins limits the protected coherence time over the range of Ω accessed here. We show that amplitude noise in Ω will dominate the dephasing for larger driving fields.PACS numbers: 76.30. Mi, 63.20.kp, 76.60.Jx The triplet spin of the nitrogen-vacancy (NV) center in diamond has become a foundational component in both quantum metrology and future quantum information technologies. For sensing, the inhomogeneous dephasing time T * 2 of an NV center spin qubit can limit sensitivity to quasi-static fields. For quantum information applications, T * 2 can limit the number and the duration of gate operations that a qubit can undergo. Pulsed dynamical decoupling (PDD) techniques based on the principle of spin echoes refocus inhomogeneous dephasing and can extend T * 2 to the homogeneous spin dephasing time T 2 or longer [1][2][3][4][5][6]. These periodic pulse sequences enable precision sensing and long-lived quantum states, but they come with drawbacks. They usually limit sensing to a narrow bandwidth and erase signal built up from quasistatic fields. Moreover, commuting echo pulses with gate operations makes decoupling during multi-qubit gates a nontrivial task [7].Continuous dynamical decoupling (CDD) offers an alternative method for prolonging T * 2 that can be used when the limitations of PDD become too restrictive. NV center CDD protocols forego the standard Zeeman spin state basis {(m s =) + 1, 0, −1} in favor of an engineered basis in which the "dressed" eigenstates are less sensitive to environmental noise than the bare spin states [8][9][10][11][12][13][14][15][16]. For an NV center spin qubit, magnetic field fluctuations from nearby paramagnetic impurities and instabilities in a magnetic bias field typically dominate dephasing. A qubit composed of dressed states designed to be more robust to these fluctuations could have a prolonged T * 2 and could be used for precision sensing of quasi-static, nonmagnetic fields such as temperature [17] or strain. For quantum information processing, CDD allows decoupling to continue during gate operations, thus protecting both...

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After 60 years: A new formula for computing quality factor is warranted

Cited by 197 publications

References 6 publications

Design and Fabrication of S<sub>0</sub> Lamb-Wave Thin-Film Lithium Niobate Micromechanical Resonators

Design and Fabrication of S<sub>0</sub> Lamb-Wave Thin-Film Lithium Niobate Micromechanical Resonators

Method of Extracting Unloaded Q Applied Across Different Resonator Technologies

Continuous dynamical decoupling of a single diamond nitrogen-vacancy center spin with a mechanical resonator

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