Let complex numbers $z _ { 1 } , z _ { 2 }$ satisfy $\left| z _ { 1 } \right| = \left| z _ { 2 } \right| = 2 , z _ { 1 } + z _ { 2 } = \sqrt { 3 } + \mathrm { i }$ , then $\left| z _ { 1 } - z _ { 2 } \right| = $ $\_\_\_\_$.