Ph.D. Thesis - Physics

More documents

Recommendations

Info

In[1]:= File: crystal_shape_6uraniborg.nb Author: Kenan Diab Calculates the structure of ion crystals in a trap using the three secular frequencies wx, wy, and wz and the number of ions n as inputs. The variables z3coeff and z4coeff are optional anharmonicity terms. everything is done is cgs units. to simplify the coulomb contribution to the energy, we divide everything by e^2, introducing the factor of 0.00131 to the harmonic part. wx 2Pi.15010^6; wy 2Pi.15010^6; wz 2Pi1.310^6; z3coeff 0; 6.7837210^10; z4coeff 0;6.5239610^11; n 13; number of ions r is the array of ion coordinates. r3i1, r3i2, r3i3 are the x,y,z coordinates of the i'th ion. rArraySubscripta,1 &,3 n; mathematica uses a relatively efficient simplex method ans NMinimize0.00063060.5wx^2Sumr3 i1^2,i, 0, n1 wy^2Sumr3 i2^2,i, 0, n1wz^2Sumr3 i3^2,i, 0, n1 z3coeffSumr3 i3^3,i, 0, n1 z4coeffSumr3 i3^4,i, 0, n1 SumSqrt1r3 i1r3 j1^2 r3 i2r3 j2^2r3 i3r3 j3^2, i, 0, n1,j, i1, n1, r, WorkingPrecision15 plot points 3D s r. Extractans, 2; points ; Fori 0, i n, i, points Appendpoints,s3 i1, s3 i2, s3 i3; ListPlot3Dpoints10 000, AspectRatioAutomatic, AxesLabel "x Μ m", "y Μ m" plot points 2D, dropping z coordinate s r. Extractans, 2; points ; Fori 0, i n, i, points Appendpoints,s3 i1, s3 i2; ListPlotpoints10 000, AspectRatio Automatic, PlotStyleRed, Thick, PointSizeLarge, AxesLabel "x Μ m", "y Μ m", PlotRange50, 50,50, 50 calculate max distance between y vals yvals ; Fori 0, in, i, yvals Appendyvals, s3 i2; dist MaxyvalsMinyvals convert energy to electron volts energy ans11.43965000000000000010^7 238
2 crystal_shape_6uraniborg.nb Out[6]= 47 640.3623492104, Out[10]= Out[14]= a1 0.00249526329454898, a20.000195872421184956, a31.0161533500737710 11 , a4 0.00189214573083234, a5 0.00137727911696546, a6 1.4059491416493810 11 , a7 0.00166082992489247, a80.00162635651624383, a9 1.7714220969052710 12 , a100.0000126775934318443, a110.00101272197346297, a12 1.4625073215769910 11 , a130.00235752128707685, a140.000687539338317872, a152.7640668945798010 12 , a16 0.000633404194797575, a17 0.00238881774381363, a187.6272368921826910 12 , a190.00134322589463185, a200.00193218179314517, a212.1748578390395210 12 , a220.00101011014777204, a23 0.0000133934171442451, a246.0450297191864710 12 , a25 0.0000164747226301317, a26 0.00101068514357131, a27 1.4970292267462410 11 , a28 0.000259410079001472, a290.00248369053655865, a301.6092050229090410 11 , a310.00218716833903424, a32 0.00101829532993938, a337.7934230481076910 12 , a34 0.00101331072935728, a350.0000157843643466466, a36 9.0404784832561810 12 , a370.00106013484503786, a38 0.00214567679997688, a391.1698311709633310 11 40 20 20 40 Out[17]= 0.00487250828037228 yΜ m 40 20 20 40 xΜ m 239
Page 1:
An Investigation of Precision and S
Page 5 and 6:
Acknowledgments What a long, strang
Page 7:
should totally start a band. I also
Page 10 and 11:
2.4 Conclusions and further questio
Page 12 and 13:
7.6.1 Regular array of stationary q
Page 15 and 16:
List of Figures 2-1 The CNOT gate i
Page 17:
7-12 Magnetic fields due to a “tr
Page 21 and 22:
Chapter 1 Introduction The growth o
Page 23 and 24:
1.1 Quantum information The concept
Page 25 and 26:
us whether the target system obeys
Page 27 and 28:
Nevertheless, there are a number of
Page 29 and 30:
Digital Analog Classical Quantum Sp
Page 31 and 32:
electrodes [TKK + 99]. This heating
Page 33 and 34:
Digital Analog Classical Quantum Sp
Page 35 and 36:
2. Initialization to a simple fiduc
Page 37 and 38:
qubits, and in Ref. [SGA + 05] in t
Page 39 and 40:
the lattice architecture, we discov
Page 41 and 42:
1.6 Contributions to this work In t
Page 43:
5) Ref. [DLC + 09b] Wiring up trapp
Page 47 and 48:
Chapter 2 Quantum simulation using
Page 49 and 50:
µN the nuclear magneton, and B0 th
Page 51 and 52:
⎡ ⎤ a 0 0 0 ⎢ ⎥ ⎢ ρ2 =
Page 53 and 54:
The same effect as number 2 above i
Page 55 and 56:
where V0 is the maximum signal stre
Page 57 and 58:
actions that occur between nuclei i
Page 59 and 60:
Figure 2-2: The 2,3-dibromothiophen
Page 61:
detail how this was done with a sim
Page 64 and 65:
and thus requires invocation of the
Page 66 and 67:
Renormalization Group (DMRG), with
Page 68 and 69:
3.3 The bounds on precision In this
Page 70 and 71:
Figure 3-1: A schematic of a generi
Page 72 and 73:
Figure 3-3: The 11.7 T, 500 MHz sup
Page 74 and 75:
. Figure 3-4: The above probe is a
Page 76 and 77:
Figure 3-5: The CHFBr2 molecule. Al
Page 78 and 79:
Figure 3-6: Frequency-domain spectr
Page 80 and 81:
used to extract the answer is irrel
Page 83 and 84:
Chapter 4 Theory and history of qua
Page 85 and 86:
GND RF r ENDCAP 0 z 0 ENDCAP Ring T
Page 87 and 88:
where Q is the charge of the trappe
Page 89 and 90:
angular momentum along the quantiza
Page 91 and 92:
emission from the excited state |
Page 93 and 94:
selection rule ∆m = ±1 is applie
Page 95 and 96:
Figure 4-3: Schematic diagram of sp
Page 97 and 98:
to address an ion in state |↑〉
Page 99 and 100:
the vibrational temperature is low.
Page 101 and 102:
to the design of the trap itself. M
Page 103 and 104:
to the quantum-mechanical ground st
Page 105 and 106:
Chapter 5 Lattice ion traps for qua
Page 107 and 108:
Figure 5-1: Schematic of the lattic
Page 109 and 110:
Figure 5-3: Fit to Eq. 5.2 of the C
Page 111 and 112:
Figure 5-4: The vacuum chamber for
Page 113 and 114:
weeks. Low pressures depend on choo
Page 115 and 116:
Figure 5-5: Left: Level diagram for
Page 117 and 118:
Figure 5-7: (a) Schematic of the cr
Page 119 and 120:
(a) Lattice Trap Schematic TOP PLAT
Page 121 and 122:
mix the microspheres evenly in the
Page 123 and 124:
Using the expression for ωˆr deri
Page 125 and 126:
Figure 5-15: Plot of the motional c
Page 127 and 128:
Figure 5-17: Dependence of the trap
Page 129 and 130:
Chapter 6 Surface-electrode PCB ion
Page 131 and 132:
Figure 6-1: Schematic of a linear i
Page 133 and 134:
Figure 6-2: Layout of the trap elec
Page 135 and 136:
Figure 6-3: Above are the cross sec
Page 137 and 138:
Figure 6-6: Photograph of the trap
Page 139 and 140:
Figure 6-8: CCD image of a cloud of
Page 141 and 142:
Figure 6-9: Measurement results sho
Page 143 and 144:
Figure 6-11: Bastille mounted in th
Page 145 and 146:
Figure 6-13: A diagram of the setup
Page 147 and 148:
Figure 6-14: A plot of the trapped
Page 149 and 150:
allows us to upper-bound the amount
Page 151 and 152:
Chapter 7 Quantum simulation in sur
Page 153 and 154:
Figure 7-1: Left: Uraniborg 1, as r
Page 155 and 156:
Figure 7-3: Calculated secular freq
Page 157 and 158:
Figure 7-5: Left: Structure of 2-D
Page 159 and 160:
Figure 7-7: Scaling of the order of
Page 161 and 162:
involved. Because ions near the cen
Page 163 and 164:
Results Before presenting the numer
Page 165 and 166:
Figure 7-10: Calculation results fo
Page 167 and 168:
7.3 Magnetic gradient forces Now th
Page 169 and 170:
Figure 7-13: Scaling of the J-coupl
Page 171 and 172:
how are single-ion operations to be
Page 173 and 174:
250 psi, which increases to around
Page 175 and 176:
Figure 7-18: At the center of this
Page 177 and 178:
Figure 7-19: The plastic socket tha
Page 179 and 180:
Figure 7-21: The two internal lense
Page 181 and 182:
Figure 7-22: Measured secular frequ
Page 183 and 184:
Along ˆy, the spacing is dˆy = 28
Page 185 and 186:
of O2 to 2 × 10 −12 torr. Decohe
Page 187 and 188: Part III Toward ion-ion coupling ov
Page 189 and 190: Chapter 8 Motivation for and theory
Page 191 and 192: Figure 8-1: Schematic of the experi
Page 193 and 194: are in close agreement in the case
Page 195 and 196: 8.2.3 Simulated coupling rates We n
Page 197 and 198: Johnson noise We begin our discussi
Page 199 and 200: should suffice. Note that the above
Page 201 and 202: Chapter 9 Measuring the interaction
Page 203 and 204: Figure 9-2: Left: Level diagram for
Page 205 and 206: Figure 9-5: Photograph of the micro
Page 207 and 208: A fit of the resulting curve return
Page 209 and 210: Figure 9-9: Linear fit of the ωˆy
Page 211 and 212: Figure 9-12: Heating rate as determ
Page 213 and 214: Chapter 10 Conclusions and outlook
Page 215 and 216: traps, linking ions using photons,
Page 217 and 218: Bibliography [ADM05] Paul M. Alsing
Page 219 and 220: [CGB + 94] J. I. Cirac, L. J. Garay
Page 221 and 222: [GME + 02] M. Greiner, O. Mandel, T
Page 223 and 224: [LCL + 07] D. R. Leibrandt, R. J. C
Page 225 and 226: [PC04a] D. Porras and J. I. Cirac.
Page 227 and 228: [TBZ05] L. Tian, R. Blatt, and P. Z
Page 229 and 230: Appendix A Matlab code for Ising mo
Page 231 and 232: err_result = mean(theerr) 231
Page 233 and 234: J = J0; Jt(1) = J; Bt(1) = B; for k
Page 235 and 236: A.3 Simulation with constant force
Page 237: Appendix B Mathematica code for ion
Page 241 and 242: Appendix C How to trap ions in a cl
Page 243 and 244: Finally, we note that the chilled w
Page 245 and 246: C.4 Laser alignment and imaging As
show all

Ph.D. Thesis - Physics

Create successful ePaper yourself

Delete template?

Save as template?