This example shows one way. If you don't want the tickmarks on the vertical line, you can remove them.
clc
close all
clear all
x = -pi:0.01:pi;
y = sin(x) + 0.01*rand(size(x));
ha(1) = subplot(1,2,1);
plot(x,y);
ha(2) = subplot(1,2,2);
plot(x,y);
linkaxes(ha, 'y'); % Link all axes in y
dx = max(x)-min(x);
midpoint = (max(x)+min(x))/2;
pos1=get(ha(1),'position');
pos2=get(ha(2),'position');
Newpos = [0.1 pos1(2)-0.1 0.8 0.05];
set(ha(1),'position',[pos1(1) pos1(2) 0.5-pos1(1) 0.75]);
set(ha(2),'position',[0.5 pos2(2) (pos1(3)+pos2(1)-pos1(1))/2 0.75]);
set(ha(1),'xlim',[x(1) midpoint]);
set(ha(2),'xlim',[midpoint x(end)]);
set(ha(1),'ylim',[min(y) max(y)]);
set(ha(2),'ylim',[min(y) max(y)]);
xmax=max(x);
xticks(ha(1),[-pi -pi*0.75 -pi*0.5 -pi*0.25 0 pi*0.25 pi*0.5 pi*0.75 pi]);
xticks(ha(2),[-pi -pi*0.75 -pi*0.5 -pi*0.25 0 pi*0.25 pi*0.5 pi*0.75 pi]);
xticklabels(ha(1),{'-\pi';'-3\pi/4';'-\pi/2';'-\pi/4';'0';'\pi/4';'\pi/2';'3\pi/4';'\pi'});
xticklabels(ha(2),{'-\pi';'-3\pi/4';'-\pi/2';'-\pi/4';'0';'\pi/4';'\pi/2';'3\pi/4';'\pi'});
S=['set(ha(2),''xlim'',get(gcbo,''value'')+[0 ' num2str(dx/2) ']);' ...
'xticks(ha(2),[-pi -pi*0.75 -pi*0.5 -pi*0.25 0 pi*0.25 pi*0.5 pi*0.75 pi]);' ...
'set(ha(1),''xlim'',get(gcbo,''value'')+[' num2str(-dx/2) ' 0]);' ...
'xticks(ha(1),[-pi -pi*0.75 -pi*0.5 -pi*0.25 0 pi*0.25 pi*0.5 pi*0.75 pi])' ...
];
%% slider which is just underneath the axis
% callback string to modify xlim of the axes
h1=uicontrol('style','slider',...
'units','normalized','position',Newpos,...
'callback',S,'min',min(x),'max',max(x));
