%% Osc period vs barrier set(0,'defaulttextInterpreter','latex') set(groot, 'defaultAxesTickLabelInterpreter','latex'); set(groot, 'defaultLegendInterpreter','latex'); %load('Z:\Tom\NAS\atomtronics\figures\osc_freq_data.mat') %text(1.3,60,'(iv)') %V_b/mu ratio Vt = [1.0000 1.0500 1.1000 1.1500 1.2000 1.2500 1.3000 1.3500 1.4000 1.4500 1.5000]; V = [1.0000 1.0500 1.1000 1.1500 1.2000 1.2500 1.3000 1.3500 1.4000 1.4500 1.5000]; %V = [1.028453293739227 1.080834273905243 1.133210535505170 1.185585233442874 1.237962810350804 1.290353750100161 1.342756509739710 1.395178340992504 1.447611161186615 1.500063881832822 1.552532404091889]; %frequencies (in ms) of the fitted orbit with a fixed initial point (-19.122,0) that give results close to yours (blue stars and red line) oscTO = [NaN NaN 52.4920 51.1320 49.7240 50.0240 49.4320 49.8000 49.1080 48.8680 48.5200]; % and your results are osc_freq = [77.5000 57.9000 52.4000 50.8000 49.7000 49.3000 49.0000 48.9000 48.8000 48.8000 48.8000]; %frequencies of the Thomas-Fermi orbit (yellow solid line) oscTF = [77.7085 69.4458 67.5354 65.1867 65.6129 65.7381 64.3689 65.2689 64.6168 63.5852 63.1496]; %frequencies of the smallest disconnected orbit (green dashed line) oscDO = [77.0037 61.8068 50.1293 42.9757 37.8005 34.2842 31.3879 30.1446 27.1919 25.8784 24.3652]; %Coordinates of the Thomas-Fermi orbit at V=1.2 in dimensionless units (yellow region) (I put only positive values of the coordinates since the rest of the points can be obtained by reflections about x or y axes) %inner boundary: xTFinner = [ 19.3893 19.3711 19.3345 19.2788 19.2353 19.2048 19.1131 18.9995 18.8824 18.8628 18.7066 18.5294 18.5222 18.3141... 18.1765 18.0742 17.8235 17.7999 17.4868 17.4706 17.1261 17.1176 16.7647 16.7054 16.4118 16.2044 16.0588 15.7059... 15.5853 15.3529 15.0000 14.7540 14.6471 14.2941 13.9412 13.5882 13.2353 13.1651 12.8824 12.5294 12.1765 11.8235... 11.7717 11.4706 11.1176 10.7647 10.4118 10.1585 10.0588 9.7059 9.3529 9.3158 9.0000 8.6786 8.6471 8.2941... 8.1485 7.9412 7.6822 7.5882 7.2544 7.2353 6.8824 6.8450 6.5294 6.4372 6.1765 6.0161 5.8235 5.5677... 5.4706 5.1176 5.0771 4.7647 4.5259 4.4118 4.0588 3.9002 3.7059 3.3529 3.1743 3.0000 2.6471 2.3002... 2.2941 1.9412 1.5882 1.2353 0.9911 0.8824 0.5294 0.1765]; yTFinner =[ 0.1765 0.5294 0.8824 1.2353 1.4397 1.5882 1.9412 2.2941 2.5962 2.6471 3.0000 3.3393 3.3529 3.7059... 3.9111 4.0588 4.3827 4.4118 4.7647 4.7817 5.1176 5.1254 5.4249 5.4706 5.6874 5.8235 5.9166 6.1165... 6.1765 6.2914 6.4413 6.5294 6.5683 6.6765 6.7629 6.8292 6.8765 6.8824 6.9072 6.9196 6.9134 6.8887... 6.8824 6.8472 6.7874 6.7079 6.6146 6.5294 6.4963 6.3589 6.1957 6.1765 6.0142 5.8235 5.8049 5.5755... 5.4706 5.3215 5.1176 5.0445 4.7647 4.7490 4.4453 4.4118 4.1406 4.0588 3.8418 3.7059 3.5547 3.3529... 3.2822 3.0284 3.0000 2.7974 2.6471 2.5790 2.3790 2.2941 2.1926 2.0210 1.9412 1.8615 1.7159 1.5882... 1.5858 1.4639 1.3611 1.2782 1.2353 1.2125 1.1641 1.1416]; %outer boundary: xTFouter = [ 0.1765 0.2408 0.5294 0.6348 0.8824 1.0530 1.2353 1.4974 1.5882 1.9412 1.9719 2.2941 2.4844 2.6471... 3.0000 3.0342 3.3529 3.6349 3.7059 4.0588 4.2945 4.4118 4.7647 5.0279 5.1176 5.4706 5.8235 5.8598... 6.1765 6.5294 6.8368 6.8824 7.2353 7.5882 7.9412 8.0527 8.2941 8.6471 9.0000 9.3529 9.7059 9.8132... 10.0588 10.4118 10.7647 11.1176 11.4706 11.8235 12.1765 12.5294 12.8824 13.2353 13.5882 13.9412 14.2941 14.6471... 15.0000 15.1263 15.3529 15.7059 16.0588 16.4118 16.7647 16.8871 17.1176 17.4706 17.8235 18.1025 18.1765 18.5294... 18.8824 19.0783 19.2353 19.5882 19.9135 19.9412 20.2941 20.6471 20.6479 21.0000 21.3056 21.3529 21.7059 21.9041... 22.0588 22.4118 22.4570 22.7647 22.9664 23.1176 23.4439 23.4706 23.8235 23.8881 24.1765 24.3050 24.5294 24.6982... 24.8824 25.0694 25.2353 25.4203 25.5882 25.7527 25.9412 26.0679 26.2941 26.3676 26.6471 26.6530 26.9210 27.0000... 27.1765 27.3529 27.4211 27.6529 27.7059 27.8715 28.0588 28.0823 28.2786 28.4118 28.4677 28.6448 28.7647 28.8144... 28.9724 29.1176 29.1250 29.2641 29.3979 29.4706 29.5230 29.6381 29.7474 29.8235 29.8492 29.9404 30.0255 30.1043... 30.1765 30.1766 30.2382 30.2933 30.3418 30.3837 30.4187 30.4468 30.4680 30.4821 30.4892]; yTFouter = [ 13.1756 13.2353 13.4956 13.5882 13.7993 13.9412 14.0881 14.2941 14.3633 14.6250 14.6471 14.8709 15.0000 15.1065... 15.3318 15.3529 15.5422 15.7059 15.7455 15.9354 16.0588 16.1177 16.2884 16.4118 16.4521 16.6037 16.7504 16.7647... 16.8841 17.0116 17.1176 17.1326 17.2417 17.3449 17.4421 17.4706 17.5292 17.6084 17.6813 17.7477 17.8075 17.8235... 17.8582 17.9014 17.9379 17.9677 17.9907 18.0068 18.0160 18.0183 18.0137 18.0022 17.9837 17.9584 17.9264 17.8876... 17.8422 17.8235 17.7881 17.7261 17.6575 17.5824 17.5011 17.4706 17.4100 17.3108 17.2056 17.1176 17.0932 16.9693... 16.8400 16.7647 16.7015 16.5532 16.4118 16.3992 16.2314 16.0593 16.0588 15.8719 15.7059 15.6791 15.4722 15.3529... 15.2563 15.0300 15.0000 14.7888 14.6471 14.5371 14.2941 14.2736 13.9937 13.9412 13.6989 13.5882 13.3890 13.2353... 13.0625 12.8824 12.7179 12.5294 12.3536 12.1765 11.9679 11.8235 11.5591 11.4706 11.1252 11.1176 10.7647 10.6582... 10.4118 10.1597 10.0588 9.7059 9.6227 9.3529 9.0406 9.0000 8.6471 8.4015 8.2941 7.9412 7.6948 7.5882... 7.2353 6.9002 6.8824 6.5294 6.1765 5.9755 5.8235 5.4706 5.1176 4.8571 4.7647 4.4118 4.0588 3.7059... 3.3534 3.3529 3.0000 2.6471 2.2941 1.9412 1.5882 1.2353 0.8824 0.5294 0.1765]; xTFouter = fliplr(xTFouter); yTFouter = fliplr(yTFouter); %Coordinates of the fitted orbit at V=1.2 in dimensionless units (blue dashed line) xTO= [ 0.0011 0.1676 0.3349 0.5038 0.6737 0.8447 1.0167 1.1901 1.3649 1.5415 1.7199 1.9007 2.0839 2.2686... 2.4539 2.6399 2.8267 3.0146 3.2030 3.3910 3.5788 3.7666 3.9539 4.1400 4.3251 4.5091 4.6915 4.8719... 5.0505 5.2271 5.4013 5.5733 5.7431 5.9105 6.0758 6.2393 6.4007 6.5608 6.7196 6.8772 7.0341 7.1905... 7.3466 7.5027 7.6588 7.8154 7.9726 8.1303 8.2891 8.4488 8.6098 8.7722 8.9361 9.1016 9.2690 9.4384... 9.6097 9.7830 9.9583 10.1359 10.3154 10.4969 10.6799 10.8645 11.0500 11.2367 11.4242 11.6128 11.8019 11.9916... 12.1817 12.3718 12.5620 12.7518 12.9414 13.1303 13.3186 13.5059 13.6922 13.8771 14.0607 14.2427 14.4233 14.6022... 14.7795 14.9547 15.1278 15.2985 15.4669 15.6329 15.7963 15.9566 16.1141 16.2686 16.4198 16.5676 16.7121 16.8532... 16.9907 17.1248 17.2554 17.3823 17.5058 17.6255 17.7415 17.8537 17.9620 18.0666 18.1666 18.2626 18.3541 18.4412... 18.5232 18.6005 18.6727 18.7400 18.8018 18.8584 18.9094 18.9554 18.9960 19.0313 19.0614 19.0862 19.1058 19.1202... 19.1294 19.1335]; yTO = [ 0.8631 0.8657 0.8737 0.8871 0.9059 0.9302 0.9596 0.9944 1.0341 1.0788 1.1283 1.1825 1.2412 1.3045... 1.3719 1.4435 1.5192 1.5988 1.6824 1.7696 1.8605 1.9551 2.0533 2.1547 2.2596 2.3679 2.4794 2.5939... 2.7116 2.8319 2.9550 3.0806 3.2085 3.3383 3.4699 3.6029 3.7368 3.8715 4.0062 4.1409 4.2748 4.4074... 4.5387 4.6676 4.7943 4.9181 5.0388 5.1559 5.2696 5.3795 5.4853 5.5874 5.6852 5.7790 5.8683 5.9537... 6.0345 6.1110 6.1825 6.2496 6.3117 6.3689 6.4208 6.4679 6.5098 6.5469 6.5789 6.6058 6.6273 6.6435... 6.6543 6.6597 6.6597 6.6543 6.6436 6.6277 6.6064 6.5799 6.5482 6.5114 6.4694 6.4223 6.3699 6.3125... 6.2500 6.1827 6.1105 6.0335 5.9514 5.8650 5.7740 5.6786 5.5786 5.4747 5.3666 5.2544 5.1384 5.0184... 4.8947 4.7671 4.6358 4.5009 4.3621 4.2196 4.0736 3.9238 3.7704 3.6136 3.4533 3.2895 3.1227 2.9529... 2.7803 2.6049 2.4274 2.2479 2.0669 1.8845 1.7010 1.5164 1.3315 1.1461 0.9606 0.7749 0.5893 0.4036... 0.2179 0.0321]; xTO = fliplr(xTO); yTO = fliplr(yTO); %Coordinates of the disconnected orbit at V=1.2 in dimensionless units (green dashed line) xDO = [ 18.5000 18.4927 18.4719 18.4376 18.3899 18.3288 18.2543 18.1667 18.0660 17.9522 17.8257 17.6868 17.5356 17.3725... 17.1981 17.0130 16.8175 16.6125 16.3983 16.1757 15.9450 15.7073 15.4625 15.2119 14.9553 14.6935 14.4269 14.1553... 13.8789 13.5984 13.3144 13.0272 12.7375 12.4460 12.1538 11.8617 11.5704 11.2804 10.9918 10.7060 10.4246 10.1481... 9.8763 9.6097 9.3486 9.0922 8.8408 8.5935 8.3503 8.1099 7.8718 7.6347 7.3973 7.1583 6.9167 6.6713... 6.4214 6.1666 5.9066 5.6420 5.3728 5.1003 4.8249 4.5482 4.2708 3.9942 3.7198 3.4476 3.1811 2.9197... 2.6671 2.4301 2.2071 1.9992 1.8239 1.6797 1.5631 1.4714 1.4114 1.3853]; yDO = [ 0 0.2865 0.5719 0.8556 1.1371 1.4162 1.6924 1.9656 2.2346 2.4988 2.7582 3.0116 3.2583 3.4981... 3.7295 3.9524 4.1654 4.3687 4.5612 4.7427 4.9131 5.0717 5.2186 5.3535 5.4763 5.5867 5.6850 5.7708... 5.8440 5.9043 5.9515 5.9854 6.0057 6.0120 6.0042 5.9825 5.9471 5.8985 5.8373 5.7629 5.6746 5.5728... 5.4584 5.3322 5.1950 5.0474 4.8902 4.7243 4.5509 4.3705 4.1846 3.9941 3.8002 3.6037 3.4061 3.2082... 3.0113 2.8165 2.6248 2.4372 2.2543 2.0771 1.9058 1.7410 1.5830 1.4320 1.2882 1.1516 1.0225 0.9007... 0.7863 0.6791 0.5788 0.4850 0.3975 0.3149 0.2363 0.1607 0.0884 0.0183]; x_in = 1.81107586192540*[[xTFinner,fliplr(-xTFinner)],fliplr([xTFinner,fliplr(-xTFinner)]),xTFinner(1)]; y_in = 1.81107586192540*[[yTFinner,fliplr(yTFinner)],fliplr([-yTFinner,fliplr(-yTFinner)]),yTFinner(1)]; x_out = 1.81107586192540*[[xTFouter,fliplr(-xTFouter)],fliplr([xTFouter,fliplr(-xTFouter)]),xTFouter(1)]; y_out = 1.81107586192540*[[yTFouter,fliplr(yTFouter)],fliplr([-yTFouter,fliplr(-yTFouter)]),yTFouter(1)]; x_TO = 1.81107586192540*[[xTO,fliplr(-xTO)],fliplr([xTO,fliplr(-xTO)]),xTO(1)]; y_TO = 1.81107586192540*[[yTO,fliplr(yTO)],fliplr([-yTO,fliplr(-yTO)]),yTO(1)]; x_DO1 = 1.81107586192540*[[xDO,fliplr(xDO)],xDO(1)]; y_DO1 = 1.81107586192540*[[yDO,fliplr(-yDO)],yDO(1)]; x_DO2 = -x_DO1; y_DO2 = y_DO1; ax2 = axes; h1 = fill([V, fliplr(V)], [oscTF, fliplr(oscDO)],'b','EdgeColor','b','FaceAlpha',0.1); hold on plot(V,oscDO,'k','linewidth',1.5) plot(V,oscTF,'k','linewidth',1.5) plot(Vt,osc_freq,'linewidth',2,'color','r'); xlabel('Barrier amplitude, $V_0/\mu$') ylabel('Oscillation period (ms)') ylim([0 80]) xlim([1 1.5]) plot(V([1:4,6:end]),oscTO([1:4,6:end]),'bs','markersize',7,'MarkerFaceColor','b') plot(V(5),oscTO(5),'.b','markersize',32) set(findall(gcf,'-property','FontSize'),'FontSize',14) ax2.Position = [0.1300 0.1256 0.7750 0.6594]; ax1 = axes; set(ax1,'color','none') ax1.Position = [0.1675 0.08 0.51 0.45]; ax1.FontSize = 12; h2 = fill(x_out, y_out ,[0.9,0.9,0.9],'EdgeColor',[0.9,0.9,0.9],'FaceAlpha',1);hold on h3 = fill(x_in, y_in ,'w','EdgeColor','k','FaceAlpha',1); plot(x_TO,y_TO,'--b','linewidth',2) plot(-x_TO(1)-0.125,y_TO(1),'.b','markersize',28) plot(x_in,y_in*0.99,'k','linewidth',1.5) plot(x_DO1,y_DO1,'k','linewidth',1.5) plot(x_DO2,y_DO2,'k','linewidth',1.5) %plot([-5,5],[-11,-11],'k','linewidth',2) %text(-4.5,-8.75,'$10\mu$m') plot([17.6,27.6],[0,0],'k','linewidth',2) text(18.1,2.5,'$10\mu$m') ax1.XTick = 0; ax1.XTickLabel = '$x$'; ax1.YTick = 0; ax1.YTickLabel = '$y$'; ax1.FontSize = 12; axis equal axis([-21*1.81107586192540 21*1.81107586192540 -7.5*1.81107586192540 7.5*1.81107586192540]) %axis off set(gcf,'color','w') exportgraphics(gcf,'Fig2.pdf','ContentType','vector') %% osc lifetime vs gamma % load('C:\Users\x2241125\Dropbox\projects\wind_transfer\time\time.mat') % gg = linspace(0,0.015,1000); % % time1 = t(:,11)'; % t1 = 0.003505*gg.^(-0.8291); % % time2 = t(:,14)'; % t2 = 0.002198*gg.^(-0.8881); % % time3 = t(:,17)'; % t3 = 0.001962*gg.^(-0.9142); % % plot(gg,t1,gg,t2,gg,t3) % ylim([0 1]) % legend('$V_b/\mu$=1','$V_b/\mu=1.15$','$V_b/\mu=1.3$') % xlabel('Damping, $\gamma$') % ylabel('Oscillation lifetime, s') % xlim([0 0.017]) % % set(findall(gcf,'-property','FontSize'),'FontSize',14)