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Les Houches, August 2015
Measurement-induced long-
distance entanglement using
optomechanical transducers
Ondřej Černotík and Klemens Hammerer
Leibniz University Hannover
Les Houches, August 2015
Mechanical oscillators can interact
with many different systems.
2
Kippenberg Lehnert
Treutlein
Sillanpää
Jayich Polzik
Les Houches, August 2015
We can use an optomechanical
system to read out the state of a qubit.
3
H = z(b + b†
) + !b†
b + g(a + a†
)(b + b†
)
Les Houches, August 2015
Performing a joint measurement on
two qubits, we can generate
entanglement between them.
4
1
z + 2
z
| 0i = (|0i + |1i)(|0i + |1i)
!
8
<
:
|00i
|11i
|01i + |10i
Hutchison et al., Canadian J. Phys. 87, 225 (2009)
Ristè et al., Nature 502, 350 (2013)
Roch et al., PRL 112, 170501 (2014)
Les Houches, August 2015
Losses and noise can be modelled
using a conditional master equation.
5
D[O]⇢ = O⇢O† 1
2 (O†
O⇢ + ⇢O†
O)
H[O]⇢ = (O hOi)⇢ + ⇢(O†
hO†
i)
d⇢ = { D[ j
] + D[ j
z]}⇢dt i [ j
z(bj + b†
j), ⇢]dt
i![b†
jbj, ⇢]dt + {(¯n + 1)D[bj] + ¯nD[b†
j]}⇢dt
ig[(aj + a†
j)(bj + b†
j), ⇢]dt

2
[a†
1a2 a1a†
2, ⇢]dt + D[a1 + a2]⇢dt
+
p
H[i(a1 + a2)]⇢dW
Les Houches, August 2015
The mechanical and optical degrees of
freedom can be adiabatically
eliminated.
6
PRA 92, 012124 (2015)
d⇢q = D[ j
]⇢qdt + D[ j
z]⇢qdt
+ D[ 1
z + 2
z]⇢qdt +
p
H[ 1
z + 2
z]⇢qdW
= 16
2
g2
!2
C =
4g2
 ¯n
> 1
Measurement rate:
Optomechanical cooperativity:
Les Houches, August 2015
We can also include optical losses.
7
Les Houches, August 2015
There is a whole range of possible
experimental realisations.
8
Anetsberger et al., Nature Physics 5, 909 (2009)
Pirkkalainen et al., Nature Commun. 6, 6981 (2015)
Les Houches, August 2015
There is a whole range of possible
experimental realisations.
9
Andrews et al., Nature Physics 10, 312 (2014)
Bagci et al., Nature 507, 81 (2014)
Pirkkalainen et al., Nature 494, 211 (2013)
Les Houches, August 2015
There is a whole range of possible
experimental realisations.
10
Rabl et al., PRB 79, 041302 (2009)
Rabl et al., Nature Physics 6, 602 (2010)
Les Houches, August 2015
Mechanical resonators are useful for
connecting different quantum systems.
11

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Measurement-induced long-distance entanglement of superconducting qubits using optomechanical transducers

  • 1. Les Houches, August 2015 Measurement-induced long- distance entanglement using optomechanical transducers Ondřej Černotík and Klemens Hammerer Leibniz University Hannover
  • 2. Les Houches, August 2015 Mechanical oscillators can interact with many different systems. 2 Kippenberg Lehnert Treutlein Sillanpää Jayich Polzik
  • 3. Les Houches, August 2015 We can use an optomechanical system to read out the state of a qubit. 3 H = z(b + b† ) + !b† b + g(a + a† )(b + b† )
  • 4. Les Houches, August 2015 Performing a joint measurement on two qubits, we can generate entanglement between them. 4 1 z + 2 z | 0i = (|0i + |1i)(|0i + |1i) ! 8 < : |00i |11i |01i + |10i Hutchison et al., Canadian J. Phys. 87, 225 (2009) Ristè et al., Nature 502, 350 (2013) Roch et al., PRL 112, 170501 (2014)
  • 5. Les Houches, August 2015 Losses and noise can be modelled using a conditional master equation. 5 D[O]⇢ = O⇢O† 1 2 (O† O⇢ + ⇢O† O) H[O]⇢ = (O hOi)⇢ + ⇢(O† hO† i) d⇢ = { D[ j ] + D[ j z]}⇢dt i [ j z(bj + b† j), ⇢]dt i![b† jbj, ⇢]dt + {(¯n + 1)D[bj] + ¯nD[b† j]}⇢dt ig[(aj + a† j)(bj + b† j), ⇢]dt  2 [a† 1a2 a1a† 2, ⇢]dt + D[a1 + a2]⇢dt + p H[i(a1 + a2)]⇢dW
  • 6. Les Houches, August 2015 The mechanical and optical degrees of freedom can be adiabatically eliminated. 6 PRA 92, 012124 (2015) d⇢q = D[ j ]⇢qdt + D[ j z]⇢qdt + D[ 1 z + 2 z]⇢qdt + p H[ 1 z + 2 z]⇢qdW = 16 2 g2 !2 C = 4g2  ¯n > 1 Measurement rate: Optomechanical cooperativity:
  • 7. Les Houches, August 2015 We can also include optical losses. 7
  • 8. Les Houches, August 2015 There is a whole range of possible experimental realisations. 8 Anetsberger et al., Nature Physics 5, 909 (2009) Pirkkalainen et al., Nature Commun. 6, 6981 (2015)
  • 9. Les Houches, August 2015 There is a whole range of possible experimental realisations. 9 Andrews et al., Nature Physics 10, 312 (2014) Bagci et al., Nature 507, 81 (2014) Pirkkalainen et al., Nature 494, 211 (2013)
  • 10. Les Houches, August 2015 There is a whole range of possible experimental realisations. 10 Rabl et al., PRB 79, 041302 (2009) Rabl et al., Nature Physics 6, 602 (2010)
  • 11. Les Houches, August 2015 Mechanical resonators are useful for connecting different quantum systems. 11