ENTANGLEMENT IN SMALL SELF-CONTAINED QUANTUM FRIDGES

NICOLAS BRUNNER, RALPH SILVA,

PAUL SKRZYPCZYK, MARCUS HUBER

NOAH LINDEN & SANDU POPESCU

SINGAPORE AUG 2013

3-QUBIT FRIDGE

3-QUBIT FRIDGE

DESIGN

3-QUBIT FRIDGE

DESIGN

INTERACTION

3-QUBIT FRIDGE

DESIGN

INTERACTION

BIAS COOLING

THE MODEL

FREE HAMILTONIAN

WITH

THE MODEL

FREE HAMILTONIAN

INTERACTION

WITH

THE MODEL

FREE HAMILTONIAN

INTERACTION

THERMALISATION

RESET QUBIT TO THERMAL STATE

WITH

THE MODEL

FREE HAMILTONIAN

INTERACTION

THERMALISATION

RESET QUBIT TO THERMAL STATE

WITH

WEAK COUPLING REGIME

SOLVING THE MODEL

MASTER EQUATION

STEADY STATE

DISSIPATOR (LINDBLAD)

TRACELESS MATRIX

≈ BIAS BETWEEN POPULATIONS OF |010> AND |101>

AROUND CARNOT POINT

STEADY STATE

TRACELESS MATRIX BIAS

AROUND CARNOT POINT

STEADY STATE

CARNOT POINT

TRACELESS MATRIX BIAS

AROUND CARNOT POINT

STEADY STATE

CARNOT POINT

ALSO TRUE AROUND CARNOT (BALL OF SEP STATES)

TRACELESS MATRIX BIAS

AROUND CARNOT POINT

ENTANGLEMENT IS DETRIMENTAL FOR EFFICIENCY

STEADY STATE

CARNOT POINT

ALSO TRUE AROUND CARNOT (BALL OF SEP STATES)

TRACELESS MATRIX BIAS

ENTANGLEMENT?

STEADY STATE

WHERE

ENTANGLEMENT?

STEADY STATE

ENTANGLEMENT WITNESSES

WHERE

MEASURE OF ENTANGLEMENT

GUHNE & SEEVINCK NJP 2010, HUBER et al. PRL 2010

ENTANGLEMENT ZOO

1. ENTANGLEMENT BETWEEN ANY BIPARTITION

2. GENUINE TRIPARTITE ENTANGLEMENT

ENTANGLEMENT ZOO

1. ENTANGLEMENT BETWEEN ANY BIPARTITION

2. GENUINE TRIPARTITE ENTANGLEMENT

DOES THIS ENTANGLEMENT PLAY ANY ROLE?

COOLING

CONSIDER A GIVEN OBJECT (QUBIT) TO BE COOLED

FIX: ENERGY, BATH (TEMPERATURE TC, COUPLING)

COOLING

CONSIDER A GIVEN OBJECT (QUBIT) TO BE COOLED

CONSIDER GIVEN RESSOURCES: HOT BATH (TH) COLD BATH (TR)

FIX: ENERGY, BATH (TEMPERATURE TC, COUPLING p1)

COOLING

CONSIDER A GIVEN OBJECT (QUBIT) TO BE COOLED

FIX: ENERGY, BATH (TEMPERATURE TC, COUPLING p1)

CONSIDER GIVEN RESSOURCES: HOT BATH (TH) COLD BATH (TR)

1. OPTIMIZE COOLING TS (LOWEST T FOR QUBIT)

FREE PARAMETERS: E2 and g, p2, p3 << Ei

COOLING

CONSIDER A GIVEN OBJECT (QUBIT) TO BE COOLED

CONSIDER GIVEN RESSOURCES: HOT BATH (TH) COLD BATH (TR)

1. OPTIMIZE COOLING TS (LOWEST T FOR QUBIT)

2. OPTIMIZE COOLING IMPOSING SEPARABILITY TS*

FREE PARAMETERS: E2 and g, p2, p3 << Ei

FIX: ENERGY, BATH (TEMPERATURE TC, COUPLING p1)

COOLING ENHANCEMENT

RELATIVE COOLING ENHANCEMENT

COOLING ENHANCEMENT

RELATIVE COOLING ENHANCEMENT

NO ENHANCEMENT

COOLING ENHANCEMENT

MONOTONOUS RELATION BTW COOLING ENHANCEMENT AND ENTANGLEMENT (CONCURRENCE)

COOLING ENHANCEMENT

MONOTONOUS RELATION BTW COOLING ENHANCEMENT AND ENTANGLEMENT (CONCURRENCE)

FUNCTIONAL RELATIONSHIP?

ENERGY TRANSPORT

ENTANGLEMENT: ENERGY IN / ENERGY OUT

OPEN QUESTIONS

• BEYOND WEAK COUPLING REGIME

• OTHER MODELS

• MACROSCOPIC FRIDGES

• HEAT ENGINES

• QUANTUM EFFECTS IN BATHS